Logo der Universität Wien

An O(n²) Time Algorithm for Alternating Büchi Games

Abstract

Computing the winning set for Büchi objectives in alternating games on graphs is a central problem in computer aided verification with a large number of applications. The long standing best known upper bound for solving the problem is Õ(n·m), where n is the number of vertices and m is the number of edges in the graph. We are the first to break the Õ(n·m) boundary by presenting a new technique that reduces the running time to O(n²). This bound also leads to O(n²) time algorithms for computing the set of almost sure winning vertices for Büchi objectives (1) in alternating games with probabilistic transitions (improving an earlier bound of Õ(n·m)), (2) in concurrent graph games with constant actions (improving an earlier bound of O(n³)), and (3) in Markov decision processes (improving for m > n⁴⸍³ an earlier bound of O(min(m¹·⁵,m·n²⸍³)). We also show that the same technique can be used to compute the maximal endcomponent decomposition of a graph in time O(n²), which is an improvement over earlier bounds for m > n⁴⸍³. Finally, we show how to maintain the winning set for Büchi objectives in alternating games under a sequence of edge insertions or a sequence of edge deletions in O(n) amortized time per operation. This is the first dynamic algorithm for this problem.

GrafikTop
Authors
GrafikTop
Citation
Category
Paper in Conference Proceedings or in Workshop Proceedings (Full Paper in Proceedings)
Event Title
ACM Symposium on Discrete Algorithms (SODA12)
Divisions
Theory and Applications of Algorithms
Event Location
Kyoto, Japan
Event Type
Conference
Event Dates
17-19 Jan, 2012
Publisher
ACM
Page Range
pp. 1386-1399
Date
2012
Export
GrafikTop
Contact us
Faculty of Computer Science
University of Vienna

Währinger Straße 29
A-1090 Vienna