10.15479/AT:IST-2011-0009
Chatterjee, Krishnendu
Krishnendu
Chatterjee0000-0002-4561-241X
Henzinger, Monika
Monika
Henzinger
An O(n2) time algorithm for alternating Büchi games
IST Austria Technical Report
IST Austria
2011
2018-12-12T11:38:59Z
2020-07-14T23:07:36Z
technical_report
https://research-explorer.app.ist.ac.at/record/5379
https://research-explorer.app.ist.ac.at/record/5379.json
2664-1690
388665 bytes
application/pdf
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 ̃O(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 ̃O(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 O(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 end-component 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.