Sidestepping Barriers for Dominating Set in Parameterized Complexity

TL;DR

This paper explores new algorithmic approaches for the Dominating Set problem across various parameters, overcoming traditional complexity barriers through approximation, larger parameters, and compression techniques.

Contribution

It introduces novel algorithms and results for Dominating Set that bypass existing complexity limits using approximation, larger parameters, and compression methods.

Findings

FPT algorithms for vertex cover and feedback edge set parameters

Approximation and parameterization trade-offs for treewidth and solution size

Compression techniques for feedback edge set parameter

Abstract

We study the classic {\sc Dominating Set} problem with respect to several prominent parameters. Specifically, we present algorithmic results that sidestep time complexity barriers by the incorporation of either approximation or larger parameterization. Our results span several parameterization regimes, including: (i,ii,iii) time/ratio-tradeoff for the parameters {\em treewidth}, {\em vertex modulator to constant treewidth} and {\em solution size}; (iv,v) FPT-algorithms for the parameters {\em vertex cover number} and {\em feedback edge set number}; and (vi) compression for the parameter {\em feedback edge set number}.