1

Contention-aware scheduling with task duplication

J. Parallel Distrib. Comput. (2011)Oliver Sinnen , Andrea To, Manpreet Kaur∗

Tai, Yu-Chang 11/23/2012

2012/11/23

2

Outline

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

2012/11/23

3

IntroductionClassic scheduling①

Contention-aware scheduling③

Duplication②

Duplication④

2012/11/23

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 ni to nj w(n) : n’s computation cost c(eij) : communication cost of edge eij E∈

2012/11/23

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)2012/11/23

6

Task scheduling background

• pred(ni)• succ(ni)

• pred(n) = (source node)∅• succ(n) = (sink node)∅

ni

nx nx nx

nxnxnxnx

nx

2012/11/23

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 ∈ P2012/11/23

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),∞].

2012/11/23

9

Introduction

Classic scheduling① (1) classic model (2) List scheduling

Contention-aware scheduling③ (1) Contention model (2) topology network

Duplication② (1) impact on the formulation

Duplication④

2012/11/23

10

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

2012/11/23

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)

2012/11/23

12

List scheduling

3 3 2 2

13 13

A B C D E F

2012/11/23

13

List scheduling with dupication

• (2)become

• (3)become

exemple

2012/11/23

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

2012/11/23

15

topology network

2012/11/23

16

Exemple(Contention model)

2012/11/23

17

Contention-aware scheduling with task duplication

2012/11/23

182012/11/23

19

exemple

2012/11/23

Contention-aware scheduling with task duplication

A C B D E

20

Complexity analyze

O(VlogV+E)

O(V)O(P)

O(1)

O(|P||V|*Algo3)

2012/11/23

21

O(P*E)

O(1)

O(V)

O(P) O(E) O(routing)

O(|P||V||E|2 (routing))

O(E)

Insertion technique

2012/11/23

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))

2012/11/23

23

Experimental evaluation

Classic scheduling① (1)

Contention-aware scheduling③ (3)

Duplication② (2)

Duplication④ (4)

LS LS-CS

D D-CS CA-D

CA-LS

2012/11/23

24

Experimental evaluation

full-duplex half-duplex

2012/11/23

25

• vs • vs

D-CSCA-DCA-LSCA-D

4 4 4

44

3

3

3

3

3

1

21

1

11 1

22

2

22

43

2012/11/23

26

4

3

12

4

31

2

4

312

43

12

2012/11/23

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

2012/11/23