---
res:
bibo_abstract:
- The computation of 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(m ⋅ √m)). We then 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. Our algorithms
are the first dynamic algorithms for this problem. We then consider another core
graph theoretic problem in verification of probabilistic systems, namely computing
the maximal end-component decomposition of a graph. We present two improved static
algorithms for the maximal end-component decomposition problem. Our first algorithm
is an O(m ⋅ √m)-time algorithm, and our second algorithm is an O(n2)-time algorithm
which is obtained using the same technique as for alternating Büchi games. Thus,
we obtain an O(min &lcu;m ⋅ √m,n2})-time algorithm improving the long-standing
O(n ⋅ m) time bound. Finally, we show how to maintain the maximal end-component
decomposition of a graph under a sequence of edge insertions or a sequence of
edge deletions in O(n) amortized time per edge deletion, and O(m) worst-case time
per edge insertion. Again, our algorithms are the first dynamic algorithms for
this problem.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Krishnendu
foaf_name: Chatterjee, Krishnendu
foaf_surname: Chatterjee
foaf_workInfoHomepage: http://www.librecat.org/personId=2E5DCA20-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0002-4561-241X
- foaf_Person:
foaf_givenName: Monika
foaf_name: Henzinger, Monika
foaf_surname: Henzinger
bibo_doi: 10.1145/2597631
bibo_issue: '3'
bibo_volume: 61
dct_date: 2014^xs_gYear
dct_language: eng
dct_publisher: ACM@
dct_title: Efficient and dynamic algorithms for alternating Büchi games and maximal
end-component decomposition@
...