Solving Cut-Problems in Quadratic Time for Graphs with Bounded Treewidth

Approximating Sparsest Cut in Graphs of Bounded Treewidth

We give the first constant-factor approximation algorithm for Sparsest-Cut with general demands in bounded treewidth graphs. In contrast to previous algorithms, which rely on the flow-cut gap and/or metric embeddings, our approach exploits the Sherali-Adams hierarchy of linear programming relaxations.

Recoloring bounded treewidth graphs

Let k be an integer. Two vertex k-colorings of a graph are adjacent if they differ on exactly one vertex. A graph is k-mixing if any proper k-coloring can be transformed into any other through a sequence of adjacent proper k-colorings. Any graph is (tw + 2)-mixing, where tw is the treewidth of the graph (Cereceda 2006). We prove that the shortest sequence between any two (tw + 2)-colorings is a...

Answer Set Solving with Bounded Treewidth Revisited

Parameterized algorithms are a way to solve hard problems more efficiently, given that a specific parameter of the input is small. In this paper, we apply this idea to the field of answer set programming (ASP). To this end, we propose two kinds of graph representations of programs to exploit their treewidth as a parameter. Treewidth roughly measures to which extent the internal structure of a p...

Dynamic Programming on Graphs with Bounded Treewidth

Time-dependent shortest paths in bounded treewidth graphs

We present a proof that the number of breakpoints in the arrival function between two terminals in graphs of treewidth $w$ is $n^{O(\log^2 w)}$ when the edge arrival functions are piecewise linear. This is an improvement on the bound of $n^{\Theta(\log n)}$ by Foschini, Hershberger, and Suri for graphs without any bound on treewidth. We provide an algorithm for calculating this arrival function...