A Decomposition-based Constraint Optimization Approach for Statically Scheduling Task Graphs with Communication Delays to Multiprocessors

Singh, Satish; Ravindran,; Keutzer,

doi:10.1109/date.2007.364567

Cited by 21 publications

(25 citation statements)

References 11 publications

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“…For each algorithm, we assess the quality of the solution it generates by dividing the optimal makespan found by CPLEX (V * ) by the makespan of the solution found by the algorithm (Ṽ * ). 24 For ST-DTDA, Tables 1-3 also show the perinstance approximation ratio obtained in step 3 of ST-DTDA execution.…”

Section: Resultsmentioning

confidence: 99%

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A Message-Passing Approach to Decentralized Parallel Machine Scheduling

Vinyals¹,

Macarthur²,

Farinelli³

et al. 2013

The Computer Journal

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This paper tackles the problem of parallelizing heterogeneous computational tasks across a number of computational nodes (aka agents) where each agent may not be able to perform all the tasks and may have different computational speeds. An equivalent problem can be found in operations research, and it is known as scheduling tasks on unrelated parallel machines (also known as R C max ). Given this equivalence observation, we present the spanning tree decentralized task distribution algorithm (ST-DTDA), the first decentralized solution to R C max . ST-DTDA achieves decomposition by means of the min-max algorithm, a member of the generalized distributive law family, that performs inference by message-passing along the edges of a graphical model (known as a junction tree). Specifically, ST-DTDA uses min-max to optimally solve an approximation of the original R C max problem that results from eliminating possible agent-task allocations until it is mapped into an acyclic structure. To eliminate those allocations that are least likely to have an impact on the solution quality, ST-DTDA uses a heuristic approach. Moreover, ST-DTDA provides a per-instance approximation ratio that guarantees that the makespan of its solution (optimal in the approximated R C max problem) is not more than a factor ρ times the makespan of the optimal of the original problem. In our empirical evaluation of ST-DTDA, we show that ST-DTDA, with a min-regret heuristic, converges to solutions that are between 78 and 95% optimal whilst providing approximation ratios lower than 3.

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Section: Resultsmentioning

confidence: 99%

“…Hence, in future, we intend to extend our approach to deal with problems with task precedence constraints (i.e. where one or more tasks may have to be completed before another task is allowed to start its processing) as in [24].…”

Section: Discussionmentioning

confidence: 99%

A Message-Passing Approach to Decentralized Parallel Machine Scheduling

Vinyals¹,

Macarthur²,

Farinelli³

et al. 2013

The Computer Journal

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“…Metzner et al [17] combined a SAT solver with real-time scheduling theory to address the problem of periodic task allocation to achieve schedulability. Satish et al [14] used a SAT solver to encode both task mapping and scheduling, and graph theoretic techniques to detect cycles and critical paths. Both [17] and [14] take task graphs as input, and only consider non-overlapped schedules with the objective of minimizing the overall schedule length (makespan).…”

Section: Related Workmentioning

confidence: 99%

“…Satish et al [14] used a SAT solver to encode both task mapping and scheduling, and graph theoretic techniques to detect cycles and critical paths. Both [17] and [14] take task graphs as input, and only consider non-overlapped schedules with the objective of minimizing the overall schedule length (makespan). Task graphs can be viewed a special case of acyclic HSDF graphs without any initial tokens, since any cycle indicates a deadlock, while cycles are allowed in a HSDF graph as long as there are non-zero number of tokens on the cycle, hence actor firing does not always have to follow edge precedence order as in task graphs.…”

Section: Related Workmentioning

confidence: 99%

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Efficient SAT-Based Mapping and Scheduling of Homogeneous Synchronous Dataflow Graphs for Throughput Optimization

Liu

Yuan

et al. 2008

2008 Real-Time Systems Symposium

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As Moore's law comes to an end, multiprocessor systems are becoming ubiquitous in today's embedded systems design. In this paper, we address the problem of mapping a Homogeneous Synchronous Dataflow (HSDF) graph onto a multiprocessor platform with the objective of maximizing system throughput. We present two optimization approaches based on branch-and-bound and SAT-solving to explore the design space of all possible actorto-processor mappings and static order schedules on each processor. In the Logic-Based Benders Decomposition (LBBD) approach, we decompose the problem into a master problem of finding a feasible actor mapping and scheduling, and a sub-problem of deadlock-checking and throughput computation. In the Integrated approach, we integrate branch-and-bound search into the SAT engine to achieve more effective search tree pruning and better scalability. Performance evaluation shows that the Integrated approach outperforms the LBBD approach by a large margin.

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