Approximation and Kernelization for Chordal Vertex Deletion

TL;DR

This paper introduces a polynomial kernel and a poly(opt) approximation algorithm for the Chordal Vertex Deletion problem, solving an open problem and advancing parameterized complexity and approximation strategies.

Contribution

It provides the first polynomial kernel for ChVD parameterized by solution size and a polynomial approximation algorithm, addressing a long-standing open problem.

Findings

Polynomial kernel for ChVD established

Poly(opt) approximation algorithm developed

Open problem from 2006 resolved

Abstract

The Chordal Vertex Deletion (ChVD) problem asks to delete a minimum number of vertices from an input graph to obtain a chordal graph. In this paper we develop a polynomial kernel for ChVD under the parameterization by the solution size, as well as poly(opt) approximation algorithm. The first result answers an open problem of Marx from 2006 [WG 2006, LNCS 4271, 37-48].