Contention-aware scheduling with task duplication J. Parallel Distrib. Comput. (2011) Oliver Sinnen ∗, Andrea To, Manpreet Kaur Tai, Yu-Chang 11/23/ /11/231

Outline Introduction Task scheduling background Classic scheduling Contention-aware scheduling Complexity analyze Experimental evaluation Conclusions 2012/11/232

Introduction Classic scheduling ① Contention-aware scheduling ③ Duplication ② Duplication ④ 2012/11/233

Task scheduling background Directed acyclic graph (DAG) G = (V, E,w, c),called a task graph nodes n ∈ V : tasks edge e ij ∈ E : communication from ni to nj w(n) : n’s computation cost c(e ij ) : communication cost of edge eij ∈ E 2012/11/234

Task scheduling background set P t s (n, P) : start time of n on processor P ∈ P t f (n, P) : finish time of n on processor P ∈ P t f (n, P) = t s (n, P) + w(n) proc(n) t f (P) = max n ∈ V:proc(n)=P { t f (n, P) } sl( ＆ ) = max n ∈ V { t f (n, proc(n)) } t f (e ij, P src, P dst ) 2012/11/235

Task scheduling background pred(n i ) succ(n i ) pred(n) = ∅ (source node) succ(n) = ∅ (sink node) nini nxnx nxnx nxnx nxnx nxnx nxnx nxnx nxnx 2012/11/236

Two conditions must be fulfilled Two Constraint (1) (2) (3) (4) if pred(n) = ∅ (n is source node) t dr (n) = t dr (n, P) = 0, for all P ∈ P 2012/11/237

Technique used Insertion technique max{A, t dr (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] = [t f (P),∞]. 2012/11/238

Introduction Classic scheduling ① (1) classic model (2) List scheduling Contention-aware scheduling ③ (1) Contention model (2) topology network Duplication ② (1) impact on the formulation Duplication ④ 2012/11/239

Classic model Traditionally, most scheduling algorithms have employed a strongly idealised model of the target parallel system,called the 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 2012/11/2310

List scheduling Using either the insertion or the end technique t s (n, P) = max{A, t dr (n, P)} t f (n, P) = t s (n, P) + w(n) 2012/11/2311

List scheduling A B C D E F 2012/11/2312

List scheduling with dupication (2)become (3)become exemple 2012/11/2313

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 2012/11/2314

topology network 2012/11/2315

Exemple(Contention model) 2012/11/2316

Contention-aware scheduling with task duplication 2012/11/2317

2012/11/2318

exemple 2012/11/2319 Contention-aware scheduling with task duplication A C B D E

Complexity analyze O(VlogV+E) O(V) O(P) O(1) O(|P||V|*Algo3) 2012/11/2320

O(P*E) O(1) O(V) O(P)O(E)O(routing) O(|P||V||E| 2 (routing)) O(E) Insertion technique 2012/11/2321

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)) 2012/11/2322

Experimental evaluation Classic scheduling ① (1) Contention-aware scheduling ③ (3) Duplication ② (2) Duplication ④ (4) 2012/11/2323

Experimental evaluation full-duplex half-duplex 2012/11/2324

vs /11/2325

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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 2012/11/2327