Contention-aware scheduling with task duplication J. Parallel Distrib. Comput. (2011) Oliver Sinnen...
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Transcript of Contention-aware scheduling with task duplication J. Parallel Distrib. Comput. (2011) Oliver Sinnen...
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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
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Outline
• Introduction• Task scheduling background• Classic scheduling• Contention-aware scheduling• Complexity analyze• Experimental evaluation• Conclusions
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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∈
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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
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Task scheduling background
• pred(ni)• succ(ni)
• pred(n) = (source node)∅• succ(n) = (sink node)∅
ni
nx nx nx
nxnxnxnx
nx
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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
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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),∞].
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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
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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
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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)
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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
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O(P*E)
O(1)
O(V)
O(P) O(E) O(routing)
O(|P||V||E|2 (routing))
O(E)
Insertion technique
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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))
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Experimental evaluation
Classic scheduling① (1)
Contention-aware scheduling③ (3)
Duplication② (2)
Duplication④ (4)
LS LS-CS
D D-CS CA-D
CA-LS
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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
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