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An exact algorithm for the sequential ordering problem and its application to switching energy minimization in compilers

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Abstract

This article presents an exact algorithm for the precedence-constrained traveling salesman problem, which is also known as the sequential ordering problem. This NP-hard problem has applications in various domains, including operational research and compilers. In this article, the problem is presented and solved in the context of minimizing switching energy in compilers. Most previous work on minimizing switching energy in the compiler domain has been limited to simple heuristics that are not guaranteed to give an optimal solution. In this work, we present an exact algorithm for solving the switching energy minimization problem using a branch-and-bound approach. The proposed algorithm is simple and intuitive, yet powerful. It is the first exact algorithm for the switching energy problem that is shown to solve real instances of the problem within a few seconds per instance. Compared to previous work in the operational research domain, the proposed algorithm is believed to be the most powerful exact algorithm that does not require a linear programming formulation. The proposed algorithm is experimentally evaluated using instances taken from a production compiler. The results show that with a time limit of 10 ms per node, the proposed algorithm optimally solves 99.8 % of the instances. It optimally solves instances with up to 598 nodes within a few seconds. The resulting switching cost is 16 % less than that produced without energy awareness and 5 % less than that produced by a commonly used heuristic.

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Notes

  1. Some MiBench benchmarks were excluded due to building problems.

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Acknowledgments

This research was partially supported by a Google Faculty Research Award granted in August 2013. The authors are extremely grateful to Prof. Roberto Montemanni of the University of Applied Sciences of Southern Switzerland for providing the experimental results reported in Sect. 6.6 for their MILP-based algorithm. The authors thank the Computer Science (CS) Department at PSUT for providing the machine that was used to perform the experimental evaluation. We specially thank Husam Abed and Waseem F. Faous from the system administration team at PSUT for the technical support they provided to us. We also thank the anonymous reviewers for their constructive comments that led to significantly improving the final version of this paper.

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  1. Princess Sumaya University for Technology, Amman, Jordan

    Ghassan Shobaki & Jafar Jamal

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  1. Ghassan Shobaki
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  2. Jafar Jamal
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Correspondence to Ghassan Shobaki.

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Shobaki, G., Jamal, J. An exact algorithm for the sequential ordering problem and its application to switching energy minimization in compilers. Comput Optim Appl 61, 343–372 (2015). https://doi.org/10.1007/s10589-015-9725-9

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