A combinatorial strongly subexponential strategy improvement algorithm for mean payoff games

• Published in: Discrete Applied Mathematics Vol. 155; no. 2; pp. 210 - 229
• Main Authors: Björklund, Henrik, Vorobyov, Sergei
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Lausanne Elsevier B.V 2007; Amsterdam Elsevier; New York, NY
• Subjects: Algorithmics. Computability. Computer arithmetics; Applied sciences; Combinatorial linear programming; Combinatorics; Combinatorics. Ordered structures; Computer science; Computer science; control theory; systems; Cyclic game; Datalogi; Datavetenskap; Decision theory. Utility theory; Ergodic partition; Exact sciences and technology; Game theory; Graph theory; Information technology; Informationsteknik; Iterative improvement; Longest shortest parth; Mathematics; Mean payoff game; Operational research and scientific management; Operational research. Management science; Parity game; Randomized subexponential algorithm; Sciences and techniques of general use; TECHNOLOGY; TEKNIKVETENSKAP; Theoretical computing; Ergodic partition; Cyclic game; Iterative improvement; Parity game; Mean payoff game; Combinatorial linear programming; Randomized subexponential algorithm; Longest shortest parth; Complexity class; Shortest path; Linear programming; Computing; Combinatorial optimization; Optimal strategy; Algorithm complexity; Player strategy; Parity; Directed graph

We suggest the first strongly subexponential and purely combinatorial algorithm for solving the mean payoff games problem. It is based on iteratively improving the longest shortest distances to a sink in a possibly cyclic directed graph. We identify a new “controlled” version of the shortest paths p...