We generalise the hyperplane separation technique (Chatterjee and Velner, 2013) from multi-dimensional mean-payoff to energy games, and achieve an algorithm for solving the latter whose running time is exponential only in the dimension, but not in the number of vertices of the game graph. This answers an open question whether energy games with arbitrary initial credit can be solved in pseudo-polynomial time for fixed dimensions 3 or larger (Chaloupka, 2013). It also improves the complexity of solving multi-dimensional energy games with given initial credit from non-elementary (Br\'azdil, Jan\v{c}ar, and Ku\v{c}era, 2010) to 2EXPTIME, thus establishing their 2EXPTIME-completeness.
@article{arxiv.1502.06875,
title = {Fixed-Dimensional Energy Games are in Pseudo-Polynomial Time},
author = {Marcin Jurdziński and Ranko Lazić and Sylvain Schmitz},
journal= {arXiv preprint arXiv:1502.06875},
year = {2021}
}
Comments
Corrected proofs in former Section 3.3 Energy Games with Given Initial Credit