NP-completeness of the linear complementarity problem
Journal of Optimization Theory and Applications
The complexity of mean payoff games on graphs
Theoretical Computer Science
Theory of hybrid systems and discrete event systems
Theory of hybrid systems and discrete event systems
Competitive Markov decision processes
Competitive Markov decision processes
Deciding the winner in parity games is in UP ∩ co-UP
Information Processing Letters
A Discrete Strategy Improvement Algorithm for Solving Parity Games
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
On Model-Checking for Fragments of µ-Calculus
CAV '93 Proceedings of the 5th International Conference on Computer Aided Verification
CONCUR '95 Proceedings of the 6th International Conference on Concurrency Theory
Automata logics, and infinite games: a guide to current research
Automata logics, and infinite games: a guide to current research
A combinatorial strongly subexponential strategy improvement algorithm for mean payoff games
Discrete Applied Mathematics
A Simple P-Matrix Linear Complementarity Problem for Discounted Games
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
Linear complementarity and p-matrices for stochastic games
PSI'06 Proceedings of the 6th international Andrei Ershov memorial conference on Perspectives of systems informatics
Simple stochastic games and p-matrix generalized linear complementarity problems
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
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The performance of two pivoting algorithms, due to Lemke and Cottle and Dantzig, is studied on linear complementarity problems (LCPs) that arise from infinite games, such as parity, average-reward, and discounted games. The algorithms have not been previously studied in the context of infinite games, and they offer alternatives to the classical strategy-improvement algorithms. The two algorithms are described purely in terms of discounted games, thus bypassing the reduction from the games to LCPs, and hence facilitating a better understanding of the algorithms when applied to games. A family of parity games is given, on which both algorithms run in exponential time, indicating that in the worst case they perform no better for parity, average-reward, or discounted games than they do for general P-matrix LCPs.