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Automatic Tuning of Collective Communication Operations in MPI

Automatic Tuning of Collective Communication Operations in MPI
Automatic Tuning of Collective Communication Operations in MPI

Automatic Tuning of Collective Communication Operations in MPI Rajesh Nishtala,Neil Patel,Kaushal Sanghavi,Kushal Chakrabarti

December2003:CS262A Final Project

Computer Science Division

University of California,Berkeley

rajeshn@https://www.wendangku.net/doc/f816334539.html,{neilp,kaushal,kushalc}@https://www.wendangku.net/doc/f816334539.html,

Abstract

In this paper we present an adaptive approach to tuning MPI collective communications algorithms.

The approach was arrived at in two separate steps.In the?rst,we observed the standard vendor im-

plementation of several collective communications operations to be naive and in?exible.To make these

operations faster and more e?cient we developed a family of algorithms for each of four collective oper-

ations that often showed impressive improvement over the standard implementations.While observing

that some of these new algorithms performed better,we also noticed that their level of performance

changed relative to each other over time.These changes persisted when we varied a number of factors

a?ecting the context of the operation,including the number of processes over which to perform the

operation,the size of the data to be communicated,and the physical cluster on which the operation

was run.These observations led us to believe that the best approach to optimizing collective commu-

nication operations is to dynamically choose best-performing algorithms based on empirical results on

recent performance.In the second step,we developed a lottery scheduler that would manage these results

and probabilistically choose a globally optimal algorithm.We observed that with a scheduler,a long-

running application would choose algorithm implementations whose performance was near the optimum

performance.

1Introduction

Over the past decade,computer systems have gotten signi?cantly faster and more powerful.One of the consequences of this rapid technological advancement,however,is that the complexity of modern systems has increased dramatically.Although most system administrators,developers,and researchers possess suf-?cient knowledge of computer science to be able to fully exploit the power of these machines,there are many problems to restricting their use to such individuals.For instance,distributed systems are widely used by scientists from?elds as diverse as physics,statistics,and chemistry.However,these users cannot be expected to manually tune either their applications or the underlying systems to fully exploit the available computational power.At the same time,however,it is important to tune these applications because the tuned versions can result in signi?cant performance improvement(up to800%in our work).[5]

In practice,distributed systems and applications are often manually and tediously tuned by professional system administrators.This approach is unfortunate because such tuning is not only very expensive but is often outpaced by the rate of technological innovation.At the same time,it is interesting to examine the notion of optimization:systems are not designed to be optimal for every possible application;indeed,they cannot be.All these problems motivate the need for a system that can automatically tune these applications based on run-time parameters.

Here,we focus on the automatic optimization of collective communication operations–the transfer of data across many processes–on distributed memory computing clusters.The complex architecture of these systems,which are characterized by the presence of a high bandwidth,low latency interconnection that net-works together many heterogeneous machines,creates signi?cant opportunity for optimization.For instance, as one can see in Table1,di?erent clusters are associated with di?erent processor speeds,physical memory sizes,and network topologies,all of which can be used to produce speci?cally tuned implementations.Even more interestingly,many hardware vendors implement their own versions of point-to-point communication software which creates the possibility of optimizing over another dimension in the tuning space.

The Message Passing Interface(MPI)is a commonly used library for inter-process communication on these systems[7].We therefore concentrate on its optimization.In fact,most scienti?c computing applications use the collective communications implemented by MPI for bulk data transfers and distribution of data across

di?erent nodes for processing.For instance,parallel scienti?c applications that perform matrix multiplica-tion could use the scatter()function in MPI to distribute submatrices to di?erent machines on the cluster, and recollect them with gather()after completion of processing.

However,the presence of such a large parameter space precludes the possibility of manual tuning and motivates the need for automatic tuning.The choice of the optimal implementation of the algorithm varies across the topology of the cluster,the number of processes in the operation,and the size of the message that we wish to transfer.In this paper we analyze four common collective communications operations:broadcast, scatter,gather,and reduce.For each of these operations we have implemented a family of implementations. These implementations vary the tree structure used to disseminate the data as well as the minimum unit of transfer(heretofore called segment size).Because the optimal choice of implementation is based on many dif-ferent run time parameters such as network load and layout of the processes within the network,we present a mechanism that will dynamically chose the correct algorithm based on the lottery scheduling mechanism[11]. The structure of this report is as follows:in Section2,we further examine the intricacies of MPI and operations on which we worked.In Section3,we discuss the variations on the di?erent implementations of the operations.We then present our experimental methodology in Section4and an initial evaluation of the data in Section5and give the motivations for a dynamic choice of algorithm.In Section6,we discuss the implementation of a lottery scheduler and present its results.We conclude with related and future work in Section7.

2Relevant Message Passing Interface(MPI)Functions

The Message Passing Interface(MPI)is used for high-performance clustered computing.Particularly popular communications using MPI involve the transfer of information between one process(the root process in the MPI context)and every other process in its communication group.These transfers,henceforth referred to as collective communication operations,are described below.

2.1Broadcast

Broadcast()is intuitively network broadcast.The root process sends the same message to all the other processes in the communication group.It is de?ned as

BROADCAST(buffer,count,datatype,root,comm):

IN/OUT buffer starting address of buffer

IN count number of entries in buffer

IN datatype data type of entries in buffer

IN root rank of broadcast root

IN comm communication group

For the purposes of this paper,we say that broadcast()is an unspecialized operation because the data received by each node is not speci?c(or specialized)to it.The spirit of this de?nition is that each process, after receiving the appropriate amount of data,need only transmit one piece of data to its receiver.

2.2Reduce

Reduce()is structurally similar to Broadcast(),but is,in fact,its inverse.Here,every process sends data to the root process–instead of the root transmitting to each process.An important,di?erence,however, is that reduce()also takes in an aggregation operation that combines the data received from each of the processes into a single data set.

REDUCE(sendbuf,recvbuf,count,datatype,op,root,comm)

OUT recvbuf address of receive buffer;significant only at root

IN sendbuf address of send buffer

IN count number of elements in send buffer

IN datatype data type of elements of send buffer

IN op aggregation operation handle

IN root rank of root process

IN comm communication group

An important feature of these aggregation operation is that they are global.In other words,these operations can be performed on all the data sent by all the processes in the communication group.For instance,the MPI interface supplies default implementations of sum,min,and max.These operations are commutative and associative,since the order in which the root receives data from the processes is not de?ned. Because of these constraints,the reduce()operation can considered unspecialized.Here,the operation corresponds to the spirit of the de?nition of unspecialization because each process,upon receipt of its senders’data,need only forward a single piece of data to the corresponding recipient.This aggregation can,in fact,be performed in arbitrary sequence because of the constraint that the aggregation function be associative and commutative.

2.3Scatter

Scatter()is the operation where the root needs to send di?erent sets of data to all processes in its com-munication group.Hence,its sendbuf is broken up into di?erent sets of data,and sendbuf is the starting point for the data that the root needs to send to process with rank i.

SCATTER(sendbuf,sendcount,sendtype,recvbuf,recvcount,recvtype,root,comm) IN sendbuf address of send buffer;significant only at root

IN sendcount number of elements sent to each process;...

IN sendtype data type of send buffer elements;...

OUT recvbuf address of receive buffer

IN recvcount number of elements in receive buffer

IN recvtype data type of receive buffer elements

IN root rank of sending process

IN comm communication group

For the purposes of this paper again,we consider scatter()to be a specialized operation because each process receives a piece of data speci?c to it.When compared to unspecialization,the spirit of specialization is essentially that nodes must transmit data speci?c to each recipient.

An example of the usage of scatter()has been provided in Section1.

2.4Gather

Gather is the exact inverse operation of Scatter.The root collects a di?erent piece of information from each of the processes in the communication group.Gather is de?ned as:

GATHER(sendbuf,sendcount,sendtype,recvbuf,recvcount,recvtype,root,comm)} IN sendbuf starting address of send buffer

IN sendcount number of elements in send buffer

IN sendtype data type of send buffer elements

OUT recvbuf address of receive buffer choice;significant only at root

IN recvcount number of elements in any single receive;...

IN recvtype data type of recv buffer elements;...

IN root rank of receiving process

IN comm communication group

We state,without further elaboration,that gather()is a specialized operation by analogy to the previously mentioned operations.

3Static Optimizations:Trees&Pipelining

For each of the operations described in Section2we have created a family of implementations.These implementations vary on the tree structure used to disseminate the data,along with the segment size.In this section,we?rst discuss the structure and rami?cations of the various trees,and continue onto describing the characteristics and importance of pipelining data through the tree structure.

Sequential Binomial

Binary Chain

Figure1:The di?erent trees used to disseminate the data.

3.1Tree Structures

In order to improve upon the existing vendor-provided implementation,we have implemented each of the previously mentioned collective communication operations on four di?erent tree structures.We expect that, for certain operations,the trees will allow better parallelization of both processing and network bandwidth usage.These four di?erent tree structures are described(as shown as directed graphs in Figure1)below.

In each of these trees,if the root process is transmitting data,every process sends to its children in the corresponding tree.On the other hand,if the root process is collecting data,every process sends to its parents in the tree.For simplicity,the following discussion focuses on the former case–the latter case follows straightforwardly.

Binary The standard binary tree is important for a number of reasons.First,it allows meaningful paral-lelization of processing and network bandwidth usage,while enforcing that no process incurs the cost of sending to more than two other processes.This network bandwidth parallelization is important because,at each time step,an increasing number of processes can use their network links to send data.Second,it limits the length of longest of chain of consecutive sends to O(lg N),where N is the number of processes in the communication group.Other scaling characteristics of this tree is similar to binomial,and is discussed below.No known standard MPI implementation uses the binary tree.1 Binomial The binomial tree extends the parallelization seen in the binary tree by(1)allowing a process to send to an increased number of nodes,and(2)creating a natural order in which these sends can take place.

With regard to the former,a process could be required to send to or receive from up to other O(lg N) processes.This is particularly meaningful for large communication groups,where a larger number of processes can begin to simultaneously use available network bandwidth(relative to binary).At the same time,if the process sends to the child with the greatest number of descendants(see Figure1)with blocking sends,it can be shown that every process receives the data at the same time.The binomial tree requires that a process receive data for all of its descendant processes in the tree,like binary.

Here,however,there is no straightforward expression for the amount of data that every node receives –in the worst case,however,a node might receive exponentially more data than it needs.As before, no additional data is sent in the special cases of broadcast()and reduce().The standard MPICH implementation uses the binomial tree for the broadcast()and reduce()operations.

1This observation is conditioned upon our inability to access the proprietary MPI implementation on the IBM Seaborg cluster.This condition holds for the remaining trees.

Figure2:E?ect of Segmenting.This plot shows the e?ect of segmenting on the Millennium Cluster.Each of the lines shows the speedup of the best segment size for each tree versus the unsegmented implementation of that tree.

Chain(Linear)The straightforward chain tree causes every process to send to the process that has the next highest identi?er.In this case,every process?rst receives the data for every process with an identi?er greater

than or equal to its own.Given this data,it cleaves the data intended for it,and forwards the remaining

data to the appropriate process.In the special cases of broadcast()and reduce(),the chain tree

does not induce any increased overhead in terms of network bandwidth.In the general case,however,

it requires the transmission of O(NM)data,where M is the size of each message.No known standard

implementation uses the chain tree.

Sequential The sequential tree is the naive tree in which the root process directly transmits data to every other process in its communication group.There are no parallelization bene?ts from this tree that are

apparent to the authors of this report.In fact,this tree seems to enforce that the root transmit

independent streams of data to each of its children in a way that precludes parallelization of both

network bandwidth and processing.The standard MPICH implementation of scatter()and gather()

uses the sequential tree.

3.2Pipelining

The observation that trees allow parallelization can be further leveraged by the use of pipelining.Such pipelining involves the(1)segmenting of messages and(2)the simultaneous non-blocking transmission and receipt of data.Messages can be segmented by breaking up the larger message into smaller segments and sending these smaller messages through the network.The main advantage of segmenting is that it allows the receiver to begin forwarding a segment while receiving another segment.

Data pipelining produces a number of signi?cant improvements.First,pipelining masks the processor and

network latencies that are known to be an important bottleneck in high-bandwidth networks,such as those found there.Second,because it allows the simultaneous transmission and receipt of data,pipelining exploits the full duplex nature of the interconnect links.Third,because these links are known to support very high throughput,they could in fact support the simultaneous transmission of data to multiple children,thereby decreasing the total time of transmission.

The pipeline for broadcast()and reduce()is very straightforward because the aggregated data is not speci?c to individual processes.We can thus leverage the parallelism of having processes receive one seg-ment of data and resend multiple copies of that same segment.Thus,network bandwidth can be readily parallelized.For reduce(),even processing can be parallelized within the network.

However in this model it is very di?cult to pipeline the scatter and gather operations because every mes-sages are not generic and must be routed properly through the network.Thus if we use anything besides a sequential tree to disseminate the information,there will be additional network tra?c and unnecessary transmission in the network.With respect to our tree implementations,intermediary nodes act as“packet forwarders”that route the data to their children–it is this procedure that is pipelined.We believe that, despite the dramatic increase of data on the network,pipelining on these operations still allows meaningful optimization through a greater number of processes simultaneously receiving and sending data.For instance, if there is su?cient bandwidth in the network,the transmission of additional data can occur without signi?-cantly increased cost,while still allowing the masking of network and processor latencies.In fact,In Section 5we will show that performance increases are indeed observed in practice.Figure3.2shows the e?ect of this segmenting

4Experimental Methodology

We have developed a variety of performance pro?lers to evaluate the performance of our implementations. These pro?lers,in particular,measure the performance of one of the collective communication operations across a range of segment sizes,message sizes,and communication group sizes.The ranges for these variables were as follows:message sizes ranged from1KB to1MB for scatter and gather,increasing by factor of4. For broadcast and reduce,the upper limit was extended to8MB.Segment sizes ranged from1KB to the size of the message,increasing by a factor of2.The size of the communication group ranged from2to32,50, and64for CITRIS,Millennium,and Seaborg,respectively,increasing by2.

Performance was measured in terms of median running time on each of the clusters.These times were measured on Millennium and Seaborg with standard MPI wall time clock interface,whereas times on CIT-RIS were measured with PAPI[1].We were required to implement the PAPI measurement on CITRIS because the resolution of standard MPI wall clock implementation is approximately4milliseconds–far too inaccurate for our measurements.Although the former measures total elapsed time between operation initiation and termination,and the latter measures processor ticks during actual execution,ie.excluding time spent outside of a context switch,we believe this di?erence to be negligible because we never directly compare absolute times across clusters.Each operation was executed for each parameter set ten times to account for experimental error.The data shown in the following graphs display the median run times of these runs.It is important to note,however,that the CITRIS and Millennium clusters do not employ load balancing and prevent the user from declaring acceptable load levels.For these reasons,experiments on these two clusters are not as repeatable as those on the Seaborg cluster.Table1shows a summary of the clusters that were used in our experiments.

5Initial Data Analysis

Although our pro?lers supported analysis of operations across a number of di?erent parameters,the entire parameter space was explored only for broadcast pro?ling.For scatter(),reduce(),gather(),we only analyzed performance across the four trees,segment sizes,and communication group sizes–message sizes and physical clusters were not varied.We did this for several reasons.First,the availability of computational resources were limited on the shared clusters and forced us to be selective in gathering data.Second,we observed from early trials that broadcast exhibited interesting variation across the entire range of parame-ters.Finally,analysis on broadcast alone simpli?ed our dataset while still providing suitable evidence that

Millennium[2]CITRIS[2]Seaborg(dense)[3]Seaborg(sparse)[3] Processor Type Pentium II Xeon Itanium2IBM Power3IBM Power3 Processor Clock Rate500-700MHz900MHz-1.3GHz375MHz375MHz Processors per Node2-42161 Physical Memory2-5GB4-5GB16-64GB16-64GB Network Topology Star(ie.symmetric links)Star Two Level Star Interconnect Type TCP/IP TCP/IP CSS CSS

Gigabit Ethernet Gigabit Ethernet

Nodes in Network5032464

Table1:Cluster Summary.This table shows a summary of the pertinent facts about the clusters used in our experiments.Note that there are two di?erent versions of the Seaborg cluster here.The Seaborg(dense) cluster is64processors across4nodes were used,while Seaborg(sparse)indicates64processors across64 nodes.Since the interconnects within the processor are presumably faster than the network we say that Seaborg(dense)is in essence a two level cluster.The?rst level is all the processors within a node while the second level is the interconnect of all the nodes.

variation in cluster environment exists.

Our data is organized as follows:Section5.1shows and analyzes the performance of each of the collective communications operations with each tree implementation ranging across the number of processes,all on the CITRIS cluster.Section5.2describes similar data for the broadcast operation across four di?erent clusters (CITRIS,Millennium,Seaborg(sparse),and Seaborg(dense)).Section5.3examines the performance of segmentation as a function of communication group size.

5.1Data Analysis Across Operations

We observed the performance of each of the four collective communications operations(broadcast,gather, scatter,gather)on the CITRIS cluster with each of the four tree implementations.Plots of these perfor-mance measurements are shown in Figure3.

There are substantial performance gains relative to the vendor implementation for broadcast(),reduce(), and gather();however,our various implementations of scatter()exhibited no improvements from the standard.Nevertheless,it is interesting to note that in every operation–including scatter()–there is an implementation that performs as well as,if not better than,the vendor implementation.For instance, the chain reduce()implementation scales independently of the number of processors,whereas the standard MPICH binomial reduce()implementation scales logarithmically.Similarly,we see that even for scatter(), the chain and binomial implementations perform just as well as the standard MPICH sequential implemen-tation.

In general,we see that specialized operations scale linearly with the number of processors,whereas sen-sible implementations of unspecialized operations scale logarithmically or independently of the number of processors.The additional constant cost for specialized sends is incurred because adding an additional node simply means sending up(or down)one additional level of the tree.With a pipelined implementation this

is constant cost per process.Extra unspecialized sends add little or no cost because including an additional node to the operation involves adding a single send or receive made in parallel with the original sends and receives.The sequential tree,moreover,incurs the cost because this parallelism is not present.

The similar performance of di?erent implementations of particular collective communication operations is signi?cant because transient network conditions could cause one implementation to suddenly perform sig-

ni?cantly better than its comparable implementation.This is particularly relevant for cases where many comparable implementations are,in fact,the best implementations:for instance,a chain scatter()could be adversely a?ected by network tra?c at node2,in which case a comparable binomial implementation could signi?cantly outperform it(see Figure3).This observation is critical to the motivation behind lottery scheduling and is discussed further in Section6.1.2.

Figure 3:Varying the Operation on CITRIS .These plots show the di?erences across operations on the CITRIS cluster.For a given number of processors the graph shows the time taken for the best segment size for each of the given trees.

5.2Data Analysis Across Clusters

The broadcast operation was run on four di?erent clusters.Figure 4shows the performance of the four tree implementations on each of these clusters.On the CITRIS and Millennium clusters,the binary tree and chain tree implementations perform the best,and are comparable with respect to each other in the time taken to complete the operation.Nevertheless for the Millennium cluster,binary tree would be preferred for broadcasting on a relatively small communication group (between 2and 32processes),while chain is always preferred over binary on CITRIS.This suggests that small changes in the network environment could result in one tree structure being better than an another for a period of time.Thus we need a way to automatically choose the optimum MPI operation based on network and processor parameters.

Similarly,we see that the binary tree implementation is the best performer on Sparse Seaborg but does relatively poorly on the Dense Seaborg.Additionally the cost of additional processes on the Sparse cluster for all algorithms but sequential tree is close to zero.This indicates that we must strive to achieve a way to make the same implementation of MPI operations use the most e?cient algorithm,regardless of which type of architecture it is installed on.This is in stark contrast to the current solution,which involves manually ?ne-tuning the implementation before installing it on a system.

One of the important observations is that the di?erent trees perform better across di?erent clusters.For example on CITRIS,the optimal chain implementations dominate the other implementations while in the other clusters the other trees take comparable times as chain.A speculation to this observation is that the CITRIS cluster is a bandwidth limited cluster while the others are not 2.The observation is that the higher fanout factor of a tree the more the send operations that get queued at some level of the software stack.

2The

reason that we believe CITRIS is bandwidth limited is the processors used in the network are signi?cantly faster than the processors used in the other clusters.The rate at which the Itanium2processors can ship data to the network cards is a lot higher than the rate at which the network cards can put the data on the link,therefore the processors are not the limiting factor.However on the other processors,this is not the case,implying that the processors themselves are the bottleneck and the network cards can send data at the same rate at which the processor can feed the network card.

Figure 4:Varying the Cluster on a Broadcast .These plots show the di?erences across clusters for a broadcast operation.For a given number of processors the graph shows the time taken for the best segment size for each of the given trees.

Thus on bandwidth limited networks the length of this send queue could be an an important factor,implying that chain has the best performance since it has the shortest queues at every processor.However when the network bandwidth is not a limiting factor the time spent in the send queues for the various segments is a negligible e?ect,implying that the parallelism that the trees can provide can be leveraged.This would explain why the chain trees dominate on CITRIS but not the other processors.

5.3Across Parameters

Pipelining the tree algorithms is most e?ective when it is done with a segment size that is agreeable with the cluster’s underlying architecture.We see from Figure 5that clusters respond in unique ways to segment sizes.On Millennium,segmenting is crucial for the broadcast on an 8MB message,where a 16KB segment performed the best for all four tree implementations.As Millennium is a processor-constrained cluster,sending with smaller segment sizes is probably necessary to utilize link bandwidth and to mask to latency created by slow processors.Figure 6shows the e?ect of segmenting on the Millennium cluster.The ?gure shows that each of the di?erent trees has di?erent valleys which imply an optimal segment size.On the other hand the same operation on CITRIS did not rely on ?ne-grain segmenting for best performance,as a 2MB segment size was optimal for all trees.On smaller message sizes,the optimal segment was observed to be half the size of the full message.Finally,we see that on Seaborg (Sparse and Dense),no single segment size was settled on as a best size across all comm group sizes.This variation in behavior with respect to segment size among the four clusters is initially surprising given that all four saw the same implementation of broadcast,chain tree,perform best.This means that even if an algorithm implementation emerges as the universal best performer,there are cluster-speci?c parameters that must be tuned to ensure the optimal performance.Thus an adaptive approach to determining the best algorithm for a given cluster would be ideal.If we could dynamically determine the best algorithm (and parameters)given the operation to execute,commgroup size,and message size,then we could avoid the repetitive re-implementation that is prevalent in current vendor-implemented systems to deliver optimal performance on physically unique clusters.An empirical approach to choosing the optimal would be preferred to a modelling approach,as models cannot

Figure 5:Varying the Cluster on a Broadcast .These plots show the di?erences across clusters for a broadcast operation.For a given number of processors the graph shows the best segment size for each of the given trees.

Figure 6:E?ect of Segment Size Across Processors .These plots show the di?erences across trees for di?erent segment sizes and di?erent numbers of processors involved in the communication

capture real-time changes in network conditions accurately.This reasoning motivated the development of a probabilistic lottery scheduler for choosing best-performing operation implementations.Needed:-some reasoning about CITRIS’s lack of segmenting and Seaborg’s?uctuation best segment-some reasoning about the heavy use of Millennium vs.light use of CITRIS and how this may a?ect latency and bandwidth

6Dynamic Optimizations:Lottery Scheduler

We have implemented a naive version of a broadcast lottery scheduler and can,using this,show performance results that consistently outperform the equivalent MPI broadcast implementation(Figure7).Similar results are expected for lottery scheduler implementations for gather()and reduce().3

6.1Theory and Implementation

6.1.1Architecture

Intuitively speaking,the lottery scheduler should be able to adapt to particular clusters and transient clus-ter conditions by preferring e?cient implementations4This,within our framework,requires that the lottery scheduler(1)occasionally explore the implementation space and attempt to discover the most e?cient implementation available to it(exploration phase),and(2)disproportionately select this most e?cient im-plementation(execution phase).In the following subsection,we describe the theory and implementation behind the development of such a lottery scheduler.

First,we explain the actual process undergone by collective communication lottery scheduling.Upon execu-tion of a speci?c collective communication operation,the originating node selects a particular implementation of the operation according to a previously de?ned probability distribution.In practice,each implementation is allocated,at any particular time,a certain number of lottery tickets–the probability that a particular implementation is chosen is exactly the ratio of the number of tickets that it holds over the total number of tickets.After having chosen the implementation,the originating node also chooses the number of times that this choice will be valid,i.e.a time-to-live(TTL),as a function of the implementation’s relative number of tickets.The originating node then transmits,according to a statically known implementation of broadcast, e.g.the vendor-supplied broadcast(),an encoding of the function choice and TTL to every other node in its communication group.Upon receipt of this encoding,every node in the communication group(1)executes the particular collective communication operation according to the speci?ed implementation,and(2)stores it and the TTL into memory.Every future call to the same operation checks if the TTL is positive:if it is, the call decrements it,and executes the same implementation;otherwise,it chooses a new implementation based upon the aforementioned protocol,and continues similarly.Throughout the execution of the operation, the lottery scheduler measures,at each node,performance characteristics that are consistent throughout the communication group,e.g.total time until completion.Based upon these measured characteristics,each node independently updates its independent ticket allocation.

6.1.2Ticket Allocation

To the extent that this ticket allocation determines the frequency at which particular implementations are chosen,the policy is critical to the sensible operation of a lottery scheduler.Early observation of this and the fact that there are a wide variety of such policies led us to implement a lottery scheduler that allows the straightforward incorporation of diverse policies.For the purposes of this report,however,we have im-plemented a simple ticket allocation policy that nevertheless performs satisfactorily in practice.The lottery scheduler,in particular,maintains for every implementation an exponential average of its running times.(It is this statistic that is updated at the end of every collective communication operation.)Based upon these averages,the lottery scheduler allocates a large proportionα,e.g.80%,of the tickets to the implementation that has the smallest average time.The remaining implementations are uniformly allocated the residual tickets.

3On the other hand,increased performance is not expected for MPI Scatter().To the extent that,(1)we have been unable to develop a better implementation of this collective communication,and(2)our lottery scheduler discovers the best implementation,it should always prefer the equivalent MPI implementation.

4Here,we de?ne an implementation of a collective communication operation to be a corresponding procedure that dissemi-nates data to the processes in its communication group according to a particular tree structure and segment size.

This ticket policy has at least a few subtle bene?ts.Most obviously,it ensures that the fastest algorithm is chosen a disproportionately high number of times.This is important because the data shows that there are a large number of algorithms that perform very poorly–this policy minimizes their negative contribution. Said in another way,this policy ensures that the average running time of lottery scheduled implementations is not a weighted average of all the algorithms;such a weighted average would be unsatisfactory because(1) there are a large number of non-optimal algorithms,and(2)these non-optimal algorithms have extremely poor running times(see Figure7).A somewhat more subtle bene?t is that this policy enforces that the lottery scheduler only improve its prediction:If a particular implementation is allocated80%of the tickets at a particular time,another implementation can be allocated80%of the tickets at a future time only if it has a faster running time.

Furthermore,every sensible lottery scheduler policy allows adaptive reaction to transient network or pro-cessor conditions.Unlike static compile-time and installation approaches,which can only utilize static performance data,lottery scheduling allows the cluster to dynamically choose the implementation that is best suited for current cluster conditions.For instance,suppose that(1)a static approach had decided upon the scatter()chain implementation,and(2)that the?rst child(process2),because of some massive transfer at the corresponding node,su?ered severe loss of bandwidth.In this case,the huge amount of data transferred through this child in scatter(),i.e.data for nodes1through N,would cause huge bottlenecks. On the other hand,a lottery scheduled approach would discover the poor performance of chain and choose, say,the binomial scatter()implementation:here,(1)process two receives only its data,and(2)cannot a?ect the performance of any other node.This is particularly relevant because the scienti?c computing op-erations that operate on such clusters generally execute for large amounts of time–this(1)simultaneously creates a huge cost for the static implementation,and(2)allows su?cient time for the lottery scheduler to discover another optimal implementation.

6.1.3Optimizations

Here,it is important to note that,over time,the lottery scheduler will?nd the implementation that,on average,is optimal.Although a theoretical analysis of this time follows,we can ensure that the lottery scheduler can rapidly choose optimal-or,at least,nearly optimal-implementations.Upon program initia-tion,the lottery scheduler reads from a prede?ned disk location,e.g.?le,previously generated exponential averages,ticket allocations,and other bookkeeping information.Lottery schedulers,throughout their execu-tion,continue to update-only within memory-this information.Upon program termination,however,the lottery scheduler writes back the updated information to this disk location.This approach has the bene?cial consequence of allowing the use of prior knowledge without signi?cant overhead:because program initiation requires several disk accesses anyways,an additional read is not particularly signi?cant;because program termination does not a?ect the performance of the program,disk accesses there are relatively inconsequen-tial.On the other hand,this allows the possibility of having di?erent programs overwrite updates from other programs,i.e.the critical section problem.We,however,believe that the steps necessary to counteract this problem are far too costly,e.g.disk writes at the completion of every operation,and consider this approach to be an appropriate balance.

In fact,the amount of time necessary for discovery of the correct implementation can be meaningfully computed according to straightforward statistical and probabilistic techniques.This characteristic is im-portant as it provides a theoretically meaningful approach to determining and optimizing the degree of responsiveness of the lottery scheduler.In general,the expected number of iterations E[I]necessary to converge to the optimal implementation is

E[I]∝|Z|lg|Z| 1?α

,

where I is the number if iterations,|Z|is the number of implementations,and(1?α)is the aforementioned probability of exploration.The intuition behind this expression lies in the observation that the lottery scheduler must“touch”every implementation some number of times.From probability theory(and the coupon collector problem),we know that,on average,|Z|lg|Z|attempts are necessary to randomly select each of|Z|items.Because the lottery scheduler will,in fact,be using non-optimal entries with probability(1?α), the lottery scheduler will iterate,on average,1

1?α

times before attempting a non-optimal implementation.

Hence,to try each of the|Z|implementations at least once,the lottery scheduler will require|Z|lg|Z|

1?α

.Finally,

Figure7:Millennium Overlay Plot.Performance of the broadcast operation as described in the previous sections with the performance of the Lottery Scheduler superimposed.

because measurements are essentially noisy observations,the lottery scheduler will need to try each of the |Z|implementations some constant(and bounded)number of times.In practice,the statistics community uses ten to?fteen observations as a general rule of thumb.

6.2Results

Looking at Figure7and Figure8,it is apparent that the lottery scheduler performs relatively well.In general,its median performance closely follows that of the optimal implementation throughout the domain. On the other hand,it is important to note that the average performance slowly diverges from the median performances of the optimal algorithm as the number of processors increase.5

This divergence is readily explained through Figure8where we can see the presence of a small num-ber of extremely poorly performing iterations.For instance,in Figure8b,we see that the overwhelming majority of lottery scheduler iterations require less than two seconds–a reasonable upper performance bound for well-performing implementations,i.e.chain and binary.The problem,however,is that a very small number of extremely poorly-performing iterations(see implementations that require more than four seconds in Figure8b)push up the average performance measurement;because there are so few calls to these implementations,the median performance measurement is not a?ected.

Although this problem cannot be entirely avoided,there are a couple improvements that warrant inspection.

5Although it might seem that we should measure median lottery scheduler performance with the other medians,this is not true.In general,a median of measurements is taken when it is believed that(1)the measurements are generated independently of each other,and(2)the presence of noisy(and extreme)measurements would inappropriately bias the actual observation. Here,however,extreme measurements are a deterministic and intended result of lottery scheduler exploration.To the end that

these extreme measurements are non-erroneous,a measurement of lottery scheduler performance should include them.

Figure 8:Performance of Lottery scheduler with 48processors.The ?rst plot shows the time taken by every iteration while the second plot shows a distribution

The most important proposal involves the allocation of exploratory tickets to non-optimal implementations in inverse proportion to their running time.Doing so acts to decrease the rate at which poor implementations are selected.This solution is,unfortunately,incomplete:it still causes the average performance of the lottery scheduler to be biased by very poorly performing implementations.For instance,in Figure 7,we see that exploration of sequential broadcast implementations would cause the inclusion of implementations that are several orders of magnitude worse than the optimal implementation.In order to circumvent this problem,we propose that the lottery scheduling algorithm only explore implementations whose running times are at most two standard deviations more than the optimal running time.This heuristic allows for the exploration of approximately optimal implementations,while precluding the implementations that are extremely poor.Although this approximation may preclude discovery of the globally optimal implementation,we believe that this could be a valid tradeo?against the tremendous cost of exploring very poor implementations.7Related Work

1.The work by Gabriel,Resch,and Rhle [4]optimize the the broadcast and reduce operations only.Moreover,they optimize only the binomial tree that is used in the MPI implementation.We improve upon this by testing with di?erent trees,as decribed in Section 3.1.

2.In [10],the automatic tuning is done by automatically re-arranging the nodes so that it matches how the cluster is structured.Also,the root dynamically sends the messages to each node informing them what they should do with the data that they have received.We improve upon this by choosing the algorithm to run by running a lottery,as decribed in Section 6.Hence,each di?erent algorigthm type gets a chance to perform well.Moreover,by calculating the time taken by an algorithm based on an exponential average,a new algorigthm type is not chosen based on a knee-jerk reaction.

3.[8]improve the existing set of MPICH implementations by optimizing the message size.However,as we explained in Section 6,this ’optimial’message size can change with changes in the environment of the cluster.As a result,automatic tuning is essential for the collective operations to perform optimally.

4.Karonis,et.al ([6])have optimized collective operations,but they have done it with a view of wide-area networks,not clusters.As a result,many of their links are much slower than the traditional high-speed clusters that we have concentrated on.

5.Shro?and Geijn have set benchmarks for common MPI operations by comparing di?erent implemen-tatins by di?erent vendors;many of which are customized for di?erent types of clusters.We believe that by letting the lottery scheduler dynamically pick the best algorithm,we have provided a generalized solution that would work well on most systems.[9].

8Future Work

?Adding di?erent types of trees.We have currently implemented the trees as a forwarding tree,i.e.: each process receives many pieces of data.It realizes if the data is meant for it,and if not,immediately passes it on to the required child process.

?Although we have optmized a few of the more oft used MPI operations,we will optimize more MPI operations,such as MPI ALLGATHER,MPI ALLREDUCE,etc.

?Extensions to the current simplistic version of Lottery Scheduler.

?Test more extensively,especially with more clusters(like Lemieux,Clerc)and di?erent interconnects like Myrinet;to make sure that the automatic tuning works across clusters,and with more varied architectures.

9Conclusion

The gains from our work emerged in two steps.In the?rst,we found the standard implementations for several MPI collective communications operations to be under-performing.To improve performance we de-veloped a family of implementations for each such operation that performed remarkably well relative to the naive implementations.In the process we observed that the algorithms behaved di?erently with respect to a variety of variables,including the operation,the size of the communication group,the size of the message, and the cluster that the operation was to run on.Additionally we found that these algorithms responded to a pipelined approach with varying degrees of success across these same variables.Reasoning about the non-uniformity of performance led us to believe that the results re?ect the fact that(1)cluster hardware architectures are diverse and thus give us little hope of?nding globally optimal implementations,and(2) conditions on networks are often unpredictably transient in nature and thus locally optimal implementa-tions may di?er over time.These observations led us to conclude that the best way to optimize collective communications in a?exible way is to adaptively choose locally optimal algorithms based on empirical data. This approach would be more?exible than the current approach of re-implementing the operations for each cluster to maintain optimal performance.The lottery scheduler was an initial attempt at achieving this goal,and its results were quite encouraging.In the future we envision that a suitably general but accurate scheduler be used across all clusters,readily incorporating new,more e?ective algorithms for the collective communications operations than the current set of tree-based implementations.

References

[1]S.Browne,J.Dongarra,N.Garner,K.London,and P.Mucci.A scalable cross-platform infrastruc-

ture for application performance tuning using hardware counters.In Proceedings of Supercomputing, November2000.

[2]UC Berkeley Millennium Cluster.https://www.wendangku.net/doc/f816334539.html,.

[3]NERSC High Performance Computing Facility,LBNL,and IBM.https://www.wendangku.net/doc/f816334539.html,/computers/sp/.

[4]E.Gabriel,M.Resch,and R.Rhle.Implementing mpi with optimized algorithms for metacomputing,

1999.

[5]Katherine A.Yelick Jack J.Dongerra,James W.Demmel.Automatic tuning for large scale scienti?c

applications.In NSF ITR Grant Proposal,2003.

[6]N.T.Karonis,B.R.de Supinski,I.Foster,W.Gropp,E.Lusk,and J.Bresnahan.Exploiting hierarchy

in parallel computer networks to optimize collective operation performance.pages377–386.

[7]Message Passing Interface Forum.MPI:A Message Passing Interface.In Proceedings of Supercomputing

’93,pages878–883.IEEE Computer Society Press,1993.

[8]Operations In Mpich.Improving the performance of collective.

[9]Mohak Shro?and Robert A.van de Geijn.Collmark:Mpi collective communication benchmark.

[10]Sathish S.Vadhiyar,Graham E.Fagg,and Jack Dongarra.Automatically tuned collective communica-

tions.pages46–46,2000.

[11]Carl A.Waldspurger and William E.Weihl.Lottery scheduling:Flexible proportional-share resource

management.In Operating Systems Design and Implementation,pages1–11,1994.

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A、生鲜系列 B、禽肉加工系列 其它公司 C、外购系列产品 2.产品要求及贴标明细(以后期顾客实际需求调整产结构) 3.产品包装 (1)包装设计标准 门店产品包装分为两个方面: A、方便顾客携带的手提袋(要求设计大方,实用,突出公司产品形像及品牌形像。 B,设计精美,档次高,卖得起价,包装吸引客户购买,增加销量,过年过节送的礼盒。(要求能突出产品档次,产品品牌形像、公司品牌形像) (2)公司产品包装单位(指门店运营过程中的计量单位) 4 .产品外购 (1)明确产品外购标准 A、市场有需求,但我司暂时未能生产的品种. B、我司产品有生产,但因未达到规模化效应或机器设备自动化程度不高,成本没有优势的产品, C、我司产能紧张,一些品种通过与生产沟通,在预算的时间内未能进行生产,为了确保货源不断货,需要对外进行采购的。 四(渠道策略 1.渠道标准 1,拥有良好位置农贸市场周边店面,以便于提升我司产品的品牌形象。 2,具备较好的周边环境,方便公司物流配送. 3,具备较高的流动人口,保持门店的视觉印象和客户资源。

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连锁店经营模式及运作管理分析

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品牌人文化。对于一个连锁企业而言,所需要的不仅是其产品的质量要好,更要求它把品牌建设作为一种文化事业来经营。连锁店需要考虑的是我们的经营和服务能够带给顾客什么样的文化内涵。而商品永远都只是基础,品牌文化才是连锁店品牌形象最主要的体现。 比如大家喜欢麦当劳,并不是因为麦当劳的汉堡特别好吃,而是因为到了麦当劳你会感到是受欢迎的,是很快乐的。而人们去星巴克,也不是因为它的咖啡好喝,实际上是去体验一种青涩的咖啡文化,这些都是连锁店实施品牌人文化的理念。 服务品牌化。一个人要有自己的核心特长,一个品牌也需要有自己的核心价值。连锁店的品牌打造是一个系统性的工程,不是一朝一日可以做得到的。但是在连锁品牌的众多要素之中,服务品牌化是可以相对快速见效的。 比如同仁堂,它里面贩卖的中药比其他同类产品价格要高,虽然其中成药能够卖高价可能与它的配方、品质以及品牌因素有关,但他们所聘请的资深专家、中医大夫所提供的药方同样也是功不可没的。 运营标准化。作为一个连锁店,我们的运营一定要有标准。如果同一个连锁品牌在不同的店面里,顾客接受的服务基本一致并认可这种服务,那么只要有这个品牌在,他首先都会想到去这个品牌连锁店购物。 比如小肥羊。小肥羊的成功要素之一就是用涮火锅的方法,摆脱了厨师的问题。小肥羊的所有门店都是是标准化运营的,它的火锅底料、包装和食材都一直是标准化执行。 连锁规模化。加盟店的数量不是万能的,但是没有数量和规模就万万不能了。在连锁企业发展初期,连锁店的数量比质量更重要,因为它要快速扩大连锁店的数量,然后争取扩张的资金,销售产品。

大足石刻(教案新部编本)

教师学科教案[ 20 – 20 学年度第__学期] 任教学科:_____________ 任教年级:_____________ 任教老师:_____________ xx市实验学校

大足石刻风景调查 重庆市渝中区望龙门小学李波 【教学目标】: 一、知识与技能目标 1、了解世界文化遗产——大足石刻,重点了解石刻的现在情况。 2、学习各类调查方式方法,撰写调查计划,并分工调查。培养学生分析和解决问题的能力。 3、复习信息搜索技术,准确、高效、全面收集相关主题资料。培养学生分析和解决问题的能力。 4、,培养合作学习的意识、技能与方法,增强团队意识。设计一份良好的问卷。 二、过程与方法目标 1、在分解调查内容的过程中,培养学生独立思考的能力以及综合运用网络资源的能力。 2、在问卷设计的过程中,提高学生动手、探究的能力及灵活运用word软件的嫩里。 3、让学生逐步形成一种喜爱质疑、努力求知的心理倾向。 三、情感、态度与价值观目标 1、培养学生团结合作、尊重他人、分享成果的良好品格。 2、培养学生鲜明的个性和创新的意识。 3、培养学生科学精神和优良品质。 【教学重点】:准确、高效、全面地收集相关主题资料。

【教学难点】:围绕调查目的分解调查内容,并综合运用相关软件的能力。 【教学方法】:情境教学法、案例分析法、小组合作探究法。【教学过程】: 一、导入: 1、上课之前,老师先请同学们来观看一段录像片(课件:大足风光片) 2、我们重庆有许多这样漂亮的风景区,大足石刻就是其中之一,大足石刻是古代先民给我们留下的瑰宝,我们如何去了解她,保护她,我们今天将运用我们所学的知识为保护我们的历史文化遗迹做出总结的贡献,同学们愿意吗? 二、新授: (一)网络调查,收集资料 1、撰写调查计划 师:同学们,你们要了解哪些关于大足石刻的信息,请你利用网络知识在互联网上进行搜索,在搜索前请撰写好总结的调查计划。 师:请同学们以小组为单位进行操作,在小组中学会分工合作,信息共享。 (教学备注:信息搜索以网上搜索引擎的使用为主,对本机、相关联计算机内的资料收集也要重视。) 2、学生进行网络调查。 (教师随机巡视,并在学生有困难的时候及时给予指导。)3、汇报成果

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品牌人文化。对于一个连锁企业而言,所需要的不仅是其产品的质量要好,更要求它把品牌建设作为一种文化事业来经营。连锁店需要考虑的是我们的经营和服务能够带给顾客什么样的文化内涵。而商品永远都只是基础,品牌文化才是连锁店品牌形象最主要的体现。 比如大家喜欢麦当劳,并不是因为麦当劳的汉堡特别好吃,而是因为到了麦当劳你会感到是受欢迎的,是很快乐的。而人们去星巴克,也不是因为它的咖啡好喝,实际上是去体验一种青涩的咖啡文化,这些都是连锁店实施品牌人文化的理念。 服务品牌化。一个人要有自己的核心特长,一个品牌也需要有自己的核心价值。连锁店的品牌打造是一个系统性的工程,不是一朝一日可以做得到的。但是在连锁品牌的众多要素之中,服务品牌化是可以相对快速见效的。 比如同仁堂,它里面贩卖的中药比其他同类产品价格要高,虽然其中成药能够卖高价可能与它的配方、品质以及品牌因素有关,但他们所聘请的资深专家、中医大夫所提供的药方同样也是功不可没的。 运营标准化。作为一个连锁店,我们的运营一定要有标准。如果同一个连锁品牌在不同的店面里,顾客接受的服务基本一致并认可这种服务,那么只要有这个品牌在,他首先都会想到去这个品牌连锁店购物。 比如小肥羊。小肥羊的成功要素之一就是用涮火锅的方法,摆脱了厨师的问题。小肥羊的所有门店都是是标准化运营的,它的火锅底料、包装和食材都一直是标准化执行。 连锁规模化。加盟店的数量不是万能的,但是没有数量和规模就万万不能了。在连锁企业发展初期,连锁店的数量比质量更重要,因为它要快速扩大连锁店的数量,然后争取扩张的资金,销售产品。

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必须针对商品层面、店铺表现层面、卖场构成层面、基本服务层面、销售层面、推广层面、顾客层面等诸多角度,借以塑造商店形象。 连锁经营必须具备的要素 ①统一的招牌。 1统一的广告。 2统一的采购。 3统一的教育。 ⑤统一的装潢。 4统一的制造。 5统一的价格。 ⑧统一的品质。 3.管理制度的展开 连锁店管理的情报体系。 有关信息包括以下: 1财务管理。 2存量管理。 3季节库存管理。

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