Contention-aware scheduling with task duplication

1. Contention-aware scheduling with task duplication J. Parallel Distrib. Comput. (2011) Oliver Sinnen ∗, Andrea To, ManpreetKaur Tai, Yu-Chang 11/23/2012

2. Outline • Introduction • Task scheduling background • Classic scheduling • Contention-aware scheduling • Complexity analyze • Experimental evaluation • Conclusions

3. Introduction

4. Task scheduling background • Directed acyclic graph (DAG) G = (V, E,w, c),called a task graph nodes n ∈ V : tasks edge eij∈ E: communication from nito nj w(n): n’scomputation cost c(eij): communication cost of edge eij ∈ E

5. Task scheduling background • set P • ts(n, P) :start time of n on processor P ∈ P • tf(n, P) :finish time of n on processor P ∈ P tf(n, P) = ts(n, P) + w(n) • proc(n) • tf (P) = maxn∈V:proc(n)=P{tf (n, P)} • sl(＆) = maxn∈V{tf(n, proc(n))} • tf (eij, Psrc, Pdst)

6. Task scheduling background • pred(ni) • succ(ni) • pred(n) = ∅ (source node) • succ(n) = ∅ (sink node)

7. Two conditions must be fulfilled Two Constraint • (1) • (2) (3) (4) if pred(n) = ∅ (n is source node) tdr(n) =tdr(n, P) = 0, for all P ∈ P

8. Technique used • Insertion technique max{A, tdr(n, P)} + w(n) ≤ B - A free node can be scheduled on processor P within the idle time interval [A, B], A, B ∈ [0,∞], i.e. an interval in which no task is executed • End technique [A, B] = [tf (P),∞].

9. Introduction

10. Classic model • Traditionally, most scheduling algorithms have employed astrongly idealised model of the target parallel system,calledthe classic model • properties: (i) local communication has zero costs (ii) communication is performed by a communication subsystem (iii) communication can be performed concurrently (iv) The communication network is fully connected • Edge Finish Time

11. List scheduling • Using either the insertion or the end technique • ts(n, P) = max{A, tdr(n, P)} • tf (n, P) = ts(n, P) + w(n)

12. List scheduling 13 13 3 2 3 2 A B C D E F

13. List scheduling with dupication • (2)become • (3)become exemple

14. Contention Model • To make task scheduling contention aware(more realistic) The awareness for contention is achieved by edge scheduling • properties: (i) local communication has zero costs (ii) communication is performed by a communication subsystem X (iii) communication can be performed concurrently X (iv) The communication network is fully connected • Edge Finish Time

15. topology network

16. Exemple(Contention model)

17. Contention-aware scheduling with task duplication

19. Contention-aware scheduling with task duplication exemple A C B D E

20. Complexity analyze O(VlogV+E) O(|P||V|*Algo3) O(V) O(P) O(1)

21. O(P*E) O(V) Insertion technique O(P) O(E) O(routing) O(E) O(|P||V||E|2 (routing)) O(1)

22. Complexity analyze • O( |P|2 |V|2 |E|2 (routing) ) • Be aware that this is the worst-case complexity, which should be significantly higher than the expected average case complexity in this case • For comparison , the second part of a contention-aware list scheduling with the insertion technique is O(|V|2 + |P| |E| 2 (routing))

23. Experimental evaluation LS LS-CS CA-LS D D-CS CA-D

24. Experimental evaluation full-duplexhalf-duplex

25. 4 4 4 2 3 2 2 1 1 3 3 1 • vs • vs 4 4 3 3 4 2 2 1 1 3 1 2 CA-D D-CS CA-D CA-LS

26. 4 4 2 3 2 1 3 1 4 4 3 2 1 3 1 2

27. Conclusions • Duplication under the contention model is significantly better than under the classic model • Task duplication is even more beneficial under the contention model than under the classic model , and this effect increases for more restricted networks • The algorithm was proposed based on state-of-the-art scheduling techniques found in task duplication algorithms and other contention-aware algorithms