Polynomial-time algorithms for energy games with special weight structures
Chatterjee K, Henzinger MH, Krinninger S, Nanongkai D. 2014. Polynomial-time algorithms for energy games with special weight structures. Algorithmica. 70(3), 457–492.
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Abstract
Energy games belong to a class of turn-based two-player infinite-duration games played on a weighted directed graph. It is one of the rare and intriguing combinatorial problems that lie in NP∩co-NP, but are not known to be in P. The existence of polynomial-time algorithms has been a major open problem for decades and apart from pseudopolynomial algorithms there is no algorithm that solves any non-trivial subclass in polynomial time. In this paper, we give several results based on the weight structures of the graph. First, we identify a notion of penalty and present a polynomial-time algorithm when the penalty is large. Our algorithm is the first polynomial-time algorithm on a large class of weighted graphs. It includes several worst-case instances on which previous algorithms, such as value iteration and random facet algorithms, require at least sub-exponential time. Our main technique is developing the first non-trivial approximation algorithm and showing how to convert it to an exact algorithm. Moreover, we show that in a practical case in verification where weights are clustered around a constant number of values, the energy game problem can be solved in polynomial time. We also show that the problem is still as hard as in general when the clique-width is bounded or the graph is strongly ergodic, suggesting that restricting the graph structure does not necessarily help.
Publishing Year
Date Published
2014-11-01
Journal Title
Algorithmica
Publisher
Springer
Volume
70
Issue
3
Page
457 - 492
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Chatterjee K, Henzinger MH, Krinninger S, Nanongkai D. Polynomial-time algorithms for energy games with special weight structures. Algorithmica. 2014;70(3):457-492. doi:10.1007/s00453-013-9843-7
Chatterjee, K., Henzinger, M. H., Krinninger, S., & Nanongkai, D. (2014). Polynomial-time algorithms for energy games with special weight structures. Algorithmica. Springer. https://doi.org/10.1007/s00453-013-9843-7
Chatterjee, Krishnendu, Monika H Henzinger, Sebastian Krinninger, and Danupon Nanongkai. “Polynomial-Time Algorithms for Energy Games with Special Weight Structures.” Algorithmica. Springer, 2014. https://doi.org/10.1007/s00453-013-9843-7.
K. Chatterjee, M. H. Henzinger, S. Krinninger, and D. Nanongkai, “Polynomial-time algorithms for energy games with special weight structures,” Algorithmica, vol. 70, no. 3. Springer, pp. 457–492, 2014.
Chatterjee K, Henzinger MH, Krinninger S, Nanongkai D. 2014. Polynomial-time algorithms for energy games with special weight structures. Algorithmica. 70(3), 457–492.
Chatterjee, Krishnendu, et al. “Polynomial-Time Algorithms for Energy Games with Special Weight Structures.” Algorithmica, vol. 70, no. 3, Springer, 2014, pp. 457–92, doi:10.1007/s00453-013-9843-7.
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arXiv 1604.08234