Space-Efficient Graph Kernelizations

TL;DR

This paper introduces space-efficient polynomial kernels for several graph problems, achieving the best known kernel sizes with minimal memory usage, advancing the practical applicability of kernelization techniques.

Contribution

It presents new space-efficient polynomial kernels for Feedback Vertex Set, Path Contraction, and Cluster Editing/Deletion, utilizing kernel cascades for optimal results.

Findings

Kernels are polynomial in parameter k and computable in polynomial time.

Achieves kernel sizes with O(poly(k) log n) bits of memory.

Uses kernel cascades to improve kernelization efficiency.

Abstract

Let $n$ be the size of a parameterized problem and $k$ the parameter. We present kernels for Feedback Vertex Set, Path Contraction and Cluster Editing/Deletion whose sizes are all polynomial in $k$ and that are computable in polynomial time and with $O(\rm{poly}(k) \log n)$ bits (of working memory). By using kernel cascades, we obtain the best known kernels in polynomial time with $O(\rm{poly}(k) \log n)$ bits.