TY - GEN
T1 - A pseudo-polynomial algorithm for mean payoff stochastic games with perfect information and a few random positions
AU - Boros, Endre
AU - Elbassioni, Khaled
AU - Gurvich, Vladimir
AU - Makino, Kazuhisa
PY - 2013
Y1 - 2013
N2 - We consider two-person zero-sum stochastic mean payoff games with perfect information, or BWR-games, given by a digraph G = (V, E), with local rewards r: E → ℝ, and three types of vertices: black VB , white V W , and random V R forming a partition of V. It is a long-standing open question whether a polynomial time algorithm for BWR-games exists, or not. In fact, a pseudo-polynomial algorithm for these games would already imply their polynomial solvability. In this paper, we show that BWR-games with a constant number of random nodes can be solved in pseudo-polynomial time. That is, for any such game with a few random nodes |VR| = O(1), a saddle point in pure stationary strategies can be found in time polynomial in |VW| + |VB|, the maximum absolute local reward R, and the common denominator of the transition probabilities.
AB - We consider two-person zero-sum stochastic mean payoff games with perfect information, or BWR-games, given by a digraph G = (V, E), with local rewards r: E → ℝ, and three types of vertices: black VB , white V W , and random V R forming a partition of V. It is a long-standing open question whether a polynomial time algorithm for BWR-games exists, or not. In fact, a pseudo-polynomial algorithm for these games would already imply their polynomial solvability. In this paper, we show that BWR-games with a constant number of random nodes can be solved in pseudo-polynomial time. That is, for any such game with a few random nodes |VR| = O(1), a saddle point in pure stationary strategies can be found in time polynomial in |VW| + |VB|, the maximum absolute local reward R, and the common denominator of the transition probabilities.
UR - http://www.scopus.com/inward/record.url?scp=84880257132&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-39206-1_19
DO - 10.1007/978-3-642-39206-1_19
M3 - Conference contribution
AN - SCOPUS:84880257132
SN - 9783642392054
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 220
EP - 231
BT - Automata, Languages, and Programming - 40th International Colloquium, ICALP 2013, Proceedings
T2 - 40th International Colloquium on Automata, Languages, and Programming, ICALP 2013
Y2 - 8 July 2013 through 12 July 2013
ER -