Feedback vertex set inspired kernel for chordal vertex deletion

Akanksha Agrawal, Daniel Lokshtanov, Pranabendu Misra, Saket Saurabh, Meirav Zehavik

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

13 Scopus citations

Abstract

Given a graph G and a parameter k, the Chordal Vertex Deletion (CVD) problem asks whether there exists a subset U V (G) of size at most k that hits all induced cycles of size at least 4. The existence of a polynomial kernel for CVD was a well-known open problem in the field of Parameterized Complexity. Recently, Jansen and Pilipczuk resolved this question affirmatively by designing a polynomial kernel for CVD of size O(k161 log58 k), and asked whether one can design a kernel of size O(k10). While we do not completely re- solve this question, we design a significantly smaller kernel of size O(k25 log14 k), inspired by the O(k2)-size kernel for Feedback Vertex Set. To obtain this result, we first design an O(optlog2 n)-factor approximation al- gorithm for CVD, which is central to our kernelization procedure. Thus, we improve upon both the kernel- ization algorithm and the approximation algorithm of Jansen and Pilipczuk. Next, we introduce the notion of the independence degree of a vertex, which is our main conceptual contribution. We believe that this notion could be useful in designing kernels for other problems.

Original languageEnglish
Title of host publication28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017
EditorsPhilip N. Klein
PublisherAssociation for Computing Machinery
Pages1383-1398
Number of pages16
ISBN (Electronic)9781611974782
DOIs
StatePublished - 1 Jan 2017
Externally publishedYes
Event28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017 - Barcelona, Spain
Duration: 16 Jan 201719 Jan 2017

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
Volume0

Conference

Conference28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017
Country/TerritorySpain
CityBarcelona
Period16/01/1719/01/17

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