10.1016/j.jcss.2017.04.005
Chatterjee, Krishnendu
Krishnendu
Chatterjee0000-0002-4561-241X
Velner, Yaron
Yaron
Velner
Hyperplane separation technique for multidimensional mean-payoff games
Academic Press
2017
2018-12-11T11:48:07Z
2020-01-21T13:22:04Z
journal_article
https://research-explorer.app.ist.ac.at/record/717
https://research-explorer.app.ist.ac.at/record/717.json
We consider finite-state and recursive game graphs with multidimensional mean-payoff objectives. In recursive games two types of strategies are relevant: global strategies and modular strategies. Our contributions are: (1) We show that finite-state multidimensional mean-payoff games can be solved in polynomial time if the number of dimensions and the maximal absolute value of weights are fixed; whereas for arbitrary dimensions the problem is coNP-complete. (2) We show that one-player recursive games with multidimensional mean-payoff objectives can be solved in polynomial time. Both above algorithms are based on hyperplane separation technique. (3) For recursive games we show that under modular strategies the multidimensional problem is undecidable. We show that if the number of modules, exits, and the maximal absolute value of the weights are fixed, then one-dimensional recursive mean-payoff games under modular strategies can be solved in polynomial time, whereas for unbounded number of exits or modules the problem is NP-hard.