Abstract
We investigate LP-polytopes generated by mean payoff games and their properties, including the existence of tight feasible solutions of bounded size. We suggest a new associated algorithm solving a linear program and transforming its solution into a solution of the game.
Research supported by the grants from the Swedish Scientific Council and the Foundation for International Cooperation in Research and Higher Education.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Björklund, H., Nilsson, O., Svensson, O., Vorobyov, S.: Controlled linear programming: Boundedness and duality. Technical Report DIMACS-2004-56, DIMACS: Center for Discrete Mathematics and Theoretical Computer Science, Rutgers University, NJ (December 2004), http://dimacs.rutgers.edu/TechnicalReports/
Björklund, H., Nilsson, O., Svensson, O., Vorobyov, S.: The controlled linear programming problem. Technical Report DIMACS-2004-41, DIMACS: Center for Discrete Mathematics and Theoretical Computer Science, Rutgers University, NJ (September 2004)
Björklund, H., Svensson, O., Vorobyov, S.: Controlled linear programming for infinite games. Technical Report DIMACS-2005-13, DIMACS: Center for Discrete Mathematics and Theoretical Computer Science, Rutgers University, NJ (April 2005)
Björklund, H., Svensson, O., Vorobyov, S.: Linear complementarity algorithms for mean payoff games. Technical Report DIMACS-2005-05, DIMACS: Center for Discrete Mathematics and Theoretical Computer Science, Rutgers University, NJ (February 2005)
Björklund, H., Vorobyov, S.: Combinatorial structure and randomized subexponential algorithms for infinite games. Theoretical Computer Science 349(3), 347–360 (2005)
Björklund, H., Vorobyov, S.: A combinatorial strongly subexponential strategy improvement algorithm for mean payoff games. Discrete Applied Mathematics (accepted, 2006); Preliminary version in: MFCS 2004. LNCS, vol. 3153, pp. 673–685. Springer, Heidelberg (to appear, 2004) DIMACS TR 2004-05
Cottle, R.W., Pang, J.-S., Stone, R.E.: The Linear Complementarity Problem. Academic Press, London (1992)
Ehrenfeucht, A., Mycielski, J.: Positional strategies for mean payoff games. International Journ. of Game Theory 8, 109–113 (1979)
Gurvich, V.A., Karzanov, A.V., Khachiyan, L.G.: Cyclic games and an algorithm to find minimax cycle means in directed graphs. U.S.S.R. Computational Mathematics and Mathematical Physics 28(5), 85–91 (1988)
Murty, K.G., Yu, F.-T.: Linear Complementarity, Linear and Nonlinear Programming. Heldermann Verlag, Berlin (1988)
Pisaruk, N.: Mean cost cyclical games. Mathematics of Operations Research 24(4), 817–828 (1999)
Schrijver, A.: Theory of Linear and Integer Programming. John Wiley and Sons, Chichester (1986)
Schrijver, A.: Combinatorial Optimization, vol. 1-3. Springer, Heidelberg (2003)
Svensson, O., Vorobyov, S.: A subexponential algorithm for a subclass of P-matrix generalized linear complementarity problems. Technical Report DIMACS-2005-20, DIMACS: Center for Discrete Mathematics and Theoretical Computer Science, Rutgers University, NJ (June 2005)
Zwick, U., Paterson, M.: The complexity of mean payoff games on graphs. Theor. Comput. Sci. 158, 343–359 (1996)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Svensson, O., Vorobyov, S. (2006). Linear Programming Polytope and Algorithm for Mean Payoff Games. In: Cheng, SW., Poon, C.K. (eds) Algorithmic Aspects in Information and Management. AAIM 2006. Lecture Notes in Computer Science, vol 4041. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11775096_8
Download citation
DOI: https://doi.org/10.1007/11775096_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-35157-3
Online ISBN: 978-3-540-35158-0
eBook Packages: Computer ScienceComputer Science (R0)