an:05682416
Zbl 1219.05187
Kneis, Joachim; M??lle, Daniel; Richter, Stefan; Rossmanith, Peter
A bound on the pathwidth of sparse graphs with applications to exact algorithms
EN
SIAM J. Discrete Math. 23, No. 1, 407-427 (2009).
00272941
2009
j
05C85 68R10 68W01
graph algorithms; graph theory; algorithm; pathwidth
The authors resented a bound of \(m/5.769+O(\log n)\) on the pathwidth of graphs with \(m\) edges. Respective path decompositions can be computed in polynomial time. Using a well-known framework for algorithms that rely on tree decompositions, this directly leads to runtime bounds of \(O^*(2^{m/5.769})\) for \texttt{Max-2SAT} and \texttt{Max-Cut}. Both algorithms require exponential space due to dynamic programming. If we agree to accept a slightly larger bound of \(m/5.217+3\), we even obtain path decompositions with a rather simple structure: all bags share a large set of common nodes. Using branching based algorithms it may be possible to solve the same problems in polynomial space and time \(O^*(2^{m/5.217})\).
I. M. Erusalimskiy (Rostov-on-Don)