Polynomial constraint satisfaction problems, graph bisection, and the Ising partition function
ACM Transactions on Algorithms (TALG)
Fixed-Parameter tractability of treewidth and pathwidth
The Multivariate Algorithmic Revolution and Beyond
Confluence in data reduction: bridging graph transformation and kernelization
CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
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We present 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 Max-2SAT and 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, this allows us to solve the same problems in polynomial space and time $O^*(2^{m/5.217})$.