2. 1 Techniques for pipelined broadcast on ethernet switched clusters SELECTED TOPICS FOR DISTRIBUTED COMPUTING [SKR 5800] DEPARTMENT OF COMMUNICATION TECHNOLOGY AND NETWORKING LECTURER: DR. NOR ASILA WATI BT ABD HAMID PREPARED BY : MUHAMAD RAFIQ BIN OSMAN METRIC NO.: GS18838 FACULTY OF COMPUTER SCIENCE AND INFORMATION TECHNOLOGY UNIVERSITY PUTRA OF MALAYSIA

3. 2 Contents  Introduction  Literature review  Problem statements  Objectives  Methodology  Cluster designs  Broadcast trees  Contention-free linear tree  Contention-free binary tree  Heuristic algorithms  Model for computing appropriate segment sizes  Experiments  Results/ finding  Conclusion

4. 3 Introduction  Broadcast = the root process sends message to all other processes in the system. Atomic broadcast algorithms Pipelined broadcast algorithms a) Apply when the case is only one broadcast operation and the broadcast message cannot be split. a) Multiple broadcast operation and the message can be split into message segments.

5. 4 Literature review  Binomial tree based pipelined broadcast algorithm have been developed [11],[13], [23],[24], and [25].  K-binomial tree algorithm [13], has shown to have better performance than traditional binomial trees.  Does not propose new pipelined broadcast schemes, otherwise the paper develop practical techniques to facilitate the deployment of pipelined broadcast on clusters connected by multiple Ethernet switches.

6. 5 Problem statements  The problem wants to be state here are: a) We have to determine the proper broadcast tree when to apply with pipelined broadcast. b) Two or more communication could be processed actively just only when they comes from different branches. c) Appropriate segment sizes must be selected because small segment size may excessive start- up overheads while large segment size may decrease pipeline efficiency.

7. 6 Objectives  The paper has few objectives to be achieved:- a) broadcasting large messages using pipelined broadcast approach. b) develop adaptive MPI routines that use different algorithms according to the message sizes. c) allowing the algorithms and the complementary algorithms for broadcasting small messages to co- exist in one MPI routine.

8. 7 Methodology  Example of path (n0 -> n3) = {(n0,s0),(s0,s1),(s1,s3),(s3,n3)}  Contention-free pattern is a pattern where no two communications in the pattern have contention. s0 s2 s3 s1 n0 n4n3 n2 n1 n5 switches machines

9. 8 Cont..(1)Broadcast trees Linear tree3-ary treeBinary tree Flat treeBinomial tree 0 1 2 3 4 5 6 7 0 12 3456 7 0 123 4567 0 1 2 3 4 5 6 7 0 1234567

10. 9 Cont..(2) Broadcast tree Height, HNodal degree, D Completion time Linear treeP 1 (X+P-1) *T(msize/X). Binary treelog2(P)2(X+log2(P)-1) *2*T(msize/X). K-ary treelogk(P)k(X+logk(P)-1) *k*T(msize/X). Binomial tree Atomic broadcastlog(P)*T(msize). Flat treeAtomic broadcast(P-1)*T(msize).

11. 10 Contention-free linear trees  All communications in contention-free linear tree must be contention-free.  G=(S U M,E) as tree graph.  S = switches, M = machines, E = edges.  P = |M| and G’ = (S,E’) as subgraph of G.  Step 1:  Start from switch that nr is connected to, perform Depth First Search (DFS) on G’.  Numbering the switches based on the DFS arrival order.  Step 2:  Numbering ni,0,ni,1,…,ni,Xi-1. Xi=0 when no machine attaching to si.

12. 11 Contention-free binary tree  Tree height affects the time to complete the operation, smallest tree height is an ideal for pipelined broadcast binary tree.  Example (i<j≤k<l and a≤b≤c≤d):  Path (mi  mj) has three components: (mi,sa), path(sa  sb) and (sb,mj).  Path (mk  ml) has three components: (mk,sc), path (sc  sd), and (sd,ml).  When a=b, communication mi  mj does not have contention with communication mk  ml since (mi,sa) and (sb,mj) are not in path (sc  sd) and vice versa.  Question: How about k-ary broadcast tree. Is there have any contention-free from up to k children?

13. 12 Heuristic algorithms  Tree[i][j] stores tree(i,j) and best[i][j] stores the height of tree(i,j).  Tree(i,j), j>i+2 is formed by having mi as the root, tree(i+1,k-1) as the left child, and tree(k,j) as the right child.  Make sure that mi  mk does not have contention with communications in tree (i+1,k-1), which ensure that the binary tree is contention-free.  Choose k with the smallest max (best[i+1][k- 1],best[k][j])+1, which minimizes tree height.  Tree[0][P-1] stores the contention-free binary tree.

14. 13 Model for computing appropriate segment sizes  The point-to-point communication performance is characterized by five parameters: 1) L = Latency 2) Os(m) = the times that the CPUs are busy sending message of size m. 3) Or(m) = the times that the CPUs are busy receiving message of size m. 4) g(m) = the minimum time interval between consecutive message (size m) transmission and receptions. 5) P = the number of processors in the system.  Os, or, and g are functions which allows the communication time of large messages to be modeled more accurately.

15. 14 Pipelined broadcast Linear treeBinary tree Completion time calculated Does not need to consider the network contention issue. Depends on tree topology. Strategy of patterncombining the times of the point-to-point communications in the critical path. the broadcast tree first sends the segment to the left child and then to the right child Formula of completion time calculation (P-1)[L(msize/X) + g(msize/X)] + (X-1)g(msize/X) A*L(msize/X) + B*g(msize/X) + 2(X-1)g(msize/X). Propagated segments in pipelined fashion. (X-1)*g(m)(X-1)*2g(m)

16. 15 Experiments  Evaluate the performance of pipelined broadcast with various broadcast trees on 100 Mbps (fast) Ethernet and 1000 Mbps (Giga-bit) Ethernet clusters with different physical topologies.  Topology (1) contains 16 machines connected by a single switch.  Topology (2),(3),(4) and (5) are 32-machine clusters with different network connectivity.  Topology (4) and (5) have same physical topology, but different node assignments.

17. 16 Cont..(1)  Machine specifications: ProcessorDell Dimension 2400 with 2.8GHz P4 Memory640 MB Disk Space40 GB Operating SystemLinux (Fedora) with 2.6.5-1.358 kernel Ethernet CardBroadcom BCM 5705 (10/100/1000 Mbps ethernet card) with driver from Broadcom. Ethernet Switches (100 Mbps) Dell PowerConnect 2224 (24-port 100 Mbps Ethernet switches). Ethernet switches (1000 Mbps) 1000 Mbps are Dell PowerConnect 2724 (24- port 1000 Mbps switches).

18. 17 Cont..(2)  Extended parameterized LogP model characterizes the system with five parameters, L(m), os(m), or(m), g(m),P.  Select range of potential sizes from 256B to 32kB.  To obtain L(m), use pingpong program to measure the round trip time for the messages of size m(RTT(m)) and derive L(m) based on formula RTT(m)=L(m)+g(m)+L(m)+g(m).  The CPU is the bottleneck with 1000 Mbps Ethernet when the message size is more than 8kB. That’s why L(m) decreases when m increases from 8 to 32kB for the 1000 Mbps.

19. 18 Cont..(3)  Sometimes the predicted optimal segment size differ from the measured sizes.  Factor: a) first, assuming that 1-port model where each node can send and receive at the link speed. The assumption holds for the clusters with 100 Mbps Ethernet, but processor cannot keep up with sending and receiving at 1000 Mbps at the same time. b) inaccuracy in the performance parameter measurements.

20. 19 Results on 100 Mbps Ethernet switched clusters  The time for binary trees is about twice the time to send single message.  The segment size does not give impact to the pipelined broadcast.  Changing from segment size of 512 Bytes to 2048 Bytes does not significantly affect the performance, especially comparison with different algorithm.

21. 20 Performance of different broadcast trees, 100 Mbps The linear tree offers the best performance when the message size is large (>=32kB). The binary tree offers the best performance when the medium sized message (8-16kB). the communication completion time for linear trees is very close to T(msize),

22. 21 Performance of different algorithms, 100 Mbps (LAM+MPICH) – topology 4 Poor performance MPICH gradually has similar performance to the pipelined broadcast with binary trees. (scatter followed by all-gather algorithm) Pipelined broadcast with linear tree is about twice as fast as MPICH.

23. 22 Performance of different algorithms, 100 Mbps (LAM+MPICH) – topology 5 Topology-unaware algorithms is sensitive to the physical topology and manifests the advantage of pipelined broadcast with contention-free trees. All algorithms in LAM and MPICH perform poorly.

24. 23 Results on 1000 Mbps Ethernet switched clusters  The linear tree performs better than binary tree when the message is larger than 1MB.  Factor: a) the processor cannot keep up with sending and receiving data at 1000 Mbps at the same time. Binary tree pipelined broadcast algorithm is less computational intensive than the linear tree algorithm. b) larger software start-up overheads in 1000 Mbps Ethernet.

25. 24 Performance with different broadcast trees, 1000 Mbps 3-ary tree is always worse than the binary tree which confirms that k>2 ary are not effective. Insufficient CPU speed significantly affect the linear tree algorithm.

26. 25 Performance for different algorithms, 1000 Mbps (LAM+MPICH) -> topology 4 The recursive-doubling algorithm introduces severe network contention and yields extremely poor performance. Although MPICH perform well, but still 64% slower than contention-free broadcast tree.

27. 26 Performance for different algorithms, 1000 Mbps (LAM+MPICH) -> topology 5 pipelined broadcast performs better than the algorithms in MPICH and LAM on 1000 Mbps clusters in all different situations. All algorithms used by LAM and MPICH incur severe network contention and perform much worse across all the message sizes. severe network contention

28. 27 Properties of pipelined broadcast algorithms  Two conditions for pipelined broadcast to be effective:- a) the software overhead for splitting large message into segments should not be excessive. b) The pipeline term must dominate the delay term.  For 100 Mbps, when the segment size≥1024 Bytes, X*T(msize/X) is within 10% of T(msize).  For 1000 Mbps, when the segment size≥8kB, X*T(msize/X) is within 10% of T(msize).

29. 28 Cont..(1)  When the message size is smaller than these thresholds, the communication start-up overheads increase more dramatically. However, optimal segment size may less than thresholds because compromise between software overhead and pipeline efficiency.  The linear tree pipelined algorithm is efficient for broadcasting on small number of processes while the binary tree algorithm may apply for large number of processes.

30. 29 Cont..(2) 100 Mbps Cluster 1000 Mbps Cluster Linear tree algorithm (recommended size of message for broadcasting) 2*(32-1)*1kB = 62kB 2*(32-1)*8kB = 496kB Binary tree algorithm (recommended size of message for broadcasting) 2*(log32-1)*1kB = 8kB 2*(log32- 1)*8kB= 64kB

31. 30 Conclusions  Modeled segment size<>measured segment size but performance model == performance measured.  Pipelined broadcast is more efficient than other commonly used broadcast algorithms on contemporary 100 Mbps and 1000 Mbps Ethernet switched clusters in many situations.  The techniques can be applied to other types of clusters.  The near-optimal broadcast performance can be achieved by irregular topology through finding and spanning tree plus apply the techniques.

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34. 33 THE ENDS  Thank you,  Question and Answer.