Kernelization, Preprocessing for Treewidth

Years and Authors of Summarized Original Work

• 2013; Bodlaender, Jansen, Kratsch

Problem Definition

This work undertakes a theoretical study of preprocessing for the NP-hard Treewidth problem of finding a tree decomposition of width at most k for a given graph G. In other words, given G and $k \in \mathbb{N}$, the question is whether G has treewidth at most k. Several efficient reduction rules are known that provably preserve the correct answer, and experimental studies show significant size reductions [3, 5]. The present results study these and further newly introduced rules and obtain upper and lower bounds within the framework of kernelization from parameterized complexity.

The general interest in computing tree decompositions is motivated by the well-understood approach of using dynamic programming on tree decompositions that is known to allow fast algorithms on graphs of bounded treewidth (but with runtime exponential in the treewidth). A bottleneck for practical applications is...