3 research outputs found
A Faster Deterministic Exponential Time Algorithm for Energy Games and Mean Payoff Games
We present an improved exponential time algorithm for Energy Games, and hence also for Mean Payoff Games. The running time of the new algorithm is O (min(m n W, m n 2^{n/2} log W)), where n is the number of vertices, m is the number of edges, and when the edge weights are integers of absolute value at most W. For small values of W, the algorithm matches the performance of the pseudopolynomial time algorithm of Brim et al. on which it is based. For W >= n2^{n/2}, the new algorithm is faster than the algorithm of Brim et al. and is currently the fastest deterministic algorithm for Energy Games and Mean Payoff Games. The new algorithm is obtained by introducing a technique of forecasting repetitive actions performed by the algorithm of Brim et al., along with the use of an edge-weight scaling technique
The Theory of Universal Graphs for Infinite Duration Games
We introduce the notion of universal graphs as a tool for constructing
algorithms solving games of infinite duration such as parity games and mean
payoff games. In the first part we develop the theory of universal graphs, with
two goals: showing an equivalence and normalisation result between different
recently introduced related models, and constructing generic value iteration
algorithms for any positionally determined objective. In the second part we
give four applications: to parity games, to mean payoff games, and to
combinations of them (in the form of disjunctions of objectives). For each of
these four cases we construct algorithms achieving or improving over the best
known time and space complexity.Comment: 43 pages, 10 figure