• Corpus ID: 238582920

The GKK Algorithm is the Fastest over Simple Mean-Payoff Games

@article{Ohlmann2021TheGA,
  title={The GKK Algorithm is the Fastest over Simple Mean-Payoff Games},
  author={Pierre Ohlmann},
  journal={ArXiv},
  year={2021},
  volume={abs/2110.04533}
}

• Pierre Ohlmann
• Published 9 October 2021
• Computer Science
• ArXiv

We study the algorithm of Gurvich, Karzanov and Khachyian (GKK algorithm) when it is ran over mean-payoff games with no simple cycle of weight zero. We propose a new symmetric analysis, lowering the O(n2N) upper-bound of Pisaruk on the number of iterations down to N+E+ +E−+1 ≤ nN + 1, where n is the number of vertices, N is the largest absolute value of a weight, and E+ and E− are respectively the largest finite energy and dual-energy values of the game. Since each iteration is computed in O(m), this improves on the state of the art pseudopolynomial O(mnN) runtime bound of Brim, Chaloupka, Doyen, Gentilini and Raskin, by taking into account the structure of the game graph. We complement our result by showing that the analysis of Dorfman, Kaplan and Zwick also applies to the GKK algorithm, which is thus also subject to the state of the art combinatorial runtime bound of O(m2n/2). 2012 ACM Subject Classification Theory of computation → Graph algorithms analysis