%0 DATA
%A K., Chatterjee
%A Thomas A., Henzinger
%A Nir, Piterman
%D 2015
%T Algorithms for Büchi Games
%U https://leicester.figshare.com/articles/Algorithms_for_B_chi_Games/10172741
%2 https://leicester.figshare.com/ndownloader/files/18333218
%K cs.GT
%K cs.LO
%X The classical algorithm for solving B\"uchi games requires time $O(n\cdot m)$ for game graphs with $n$ states and $m$ edges. For game graphs with constant outdegree, the best known algorithm has running time $O(n^2/\log n)$. We present two new algorithms for B\"uchi games. First, we give an algorithm that performs at most $O(m)$ more work than the classical algorithm, but runs in time O(n) on infinitely many graphs of constant outdegree on which the classical algorithm requires time $O(n^2)$. Second, we give an algorithm with running time $O(n\cdot m\cdot\log\delta(n)/\log n)$, where $1\le\delta(n)\le n$ is the outdegree of the game graph. Note that this algorithm performs asymptotically better than the classical algorithm if $\delta(n)=O(\log n)$.