2013/03/13 by Andrey Grinshpun, A. Grinshpun, Grinshpun, A. +9
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Artificial Intelligence in Games #Computer Science and Game Theory (cs.GT) #Data Structures and Algorithms (cs.DS) #F.2.2 #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #cs.DS #cs.GT #cs.LO
paper · pdf · doi:10.48550/arxiv.1303.3777
27 pages, 1 figure
openalex publication_date 2013/03/13 · arxiv created 2013/07/23 · arxiv updated 2013/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Muller games are played by two players moving a token along a graph; the winner is determined by the set of vertices that occur infinitely often. The central algorithmic problem is to compute the winning regions for the players. Different classes and representations of Muller games lead to problems of varying computational complexity. One such class are parity games; these are of particular significance in computational complexity, as they remain one of the few combinatorial problems known to be in NP and co-NP but not known to be in P. We show that winning regions for a Muller game can be determined from the alternating structure of its traps. To every Muller game we then associate a natural number that we call its trap-depth; this parameter measures how complicated the trap structure is. We present algorithms for parity games that run in polynomial time for graphs of bounded trap depth, and in general run in time exponential in the trap depth.