A Polynomial Kernel For Multicut In Trees

TL;DR

This paper proves that the MULTICUT IN TREES problem admits a polynomial kernel, resolving an open question about the problem's kernelization complexity and advancing understanding of fixed-parameter tractability in graph problems.

Contribution

The authors demonstrate that MULTICUT IN TREES has a polynomial kernel, answering an open question and improving upon previous exponential kernel results.

Findings

Established polynomial kernel for MULTICUT IN TREES

Resolved an open question in kernelization complexity

Enhanced understanding of fixed-parameter algorithms for tree problems

Abstract

The MULTICUT IN TREES problem consists in deciding, given a tree, a set of requests (i.e. paths in the tree) and an integer k, whether there exists a set of k edges cutting all the requests. This problem was shown to be FPT by Guo and Niedermeyer. They also provided an exponential kernel. They asked whether this problem has a polynomial kernel. This question was also raised by Fellows. We show that MULTICUT IN TREES has a polynomial kernel.