Completely unimodal numberings of a simple polytope
Discrete Applied Mathematics
Introduction to algorithms
Cyclic games and an algorithm to find minimax cycle means in directed graphs
USSR Computational Mathematics and Mathematical Physics
Tree automata, Mu-Calculus and determinacy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
A subexponential randomized simplex algorithm (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
A subexponential bound for linear programming
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
The complexity of stochastic games
Information and Computation
A subexponential randomized algorithm for the simple stochastic game problem
Information and Computation
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
Mathematics of Operations Research
A Discrete Subexponential Algorithm for Parity Games
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
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
Memoryless determinacy of parity and mean payoff games: a simple proof
Theoretical Computer Science
Combinatorial structure and randomized subexponential algorithms for infinite games
Theoretical Computer Science
Cyclic games and linear programming
Discrete Applied Mathematics
An Optimal Strategy Improvement Algorithm for Solving Parity and Payoff Games
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
Games through Nested Fixpoints
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Linear Complementarity Algorithms for Infinite Games
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
Linear complementarity and p-matrices for stochastic games
PSI'06 Proceedings of the 6th international Andrei Ershov memorial conference on Perspectives of systems informatics
Solving parity games in big steps
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
On the equilibria of alternating move games
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Non-oblivious strategy improvement
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
Faster algorithms for mean-payoff games
Formal Methods in System Design
Linear programming polytope and algorithm for mean payoff games
AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management
A subexponential lower bound for the random facet algorithm for parity games
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
A pumping algorithm for ergodic stochastic mean payoff games with perfect information
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Tropical linear-fractional programming and parametric mean payoff games
Journal of Symbolic Computation
Polynomial-Time algorithms for energy games with special weight structures
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
The level set method for the two-sided max-plus eigenproblem
Discrete Event Dynamic Systems
A superpolynomial lower bound for strategy iteration based on snare memorization
Discrete Applied Mathematics
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
The complexity of infinitely repeated alternating move games
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
A note on the approximation of mean-payoff games
Information Processing Letters
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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 problem. By selecting exactly one outgoing edge in each of the controlled vertices we want to make the shortest distances from all vertices to the unique sink as long as possible. The decision version of the problem (whether the shortest distance from a given vertex can be made bigger than a given bound?) belongs to the complexity class NP@?CONP. Mean payoff games are easily reducible to this problem. We suggest an algorithm for computing longest shortest paths. Player MAX selects a strategy (one edge from each controlled vertex) and player MIN responds by evaluating shortest paths to the sink in the remaining graph. Then MAX locally changes choices in controlled vertices looking at attractive switches that seem to increase shortest paths lengths (under the current evaluation). We show that this is a monotonic strategy improvement, and every locally optimal strategy is globally optimal. This allows us to construct a randomized algorithm of complexity min(poly.W,2^O^(^n^l^o^g^n^)), which is simultaneously pseudopolynomial (W is the maximal absolute edge weight) and subexponential in the number of vertices n. All previous algorithms for mean payoff games were either exponential or pseudopolynomial (which is purely exponential for exponentially large edge weights).