Rank vertex cover as a natural problem for algebraic compression

Syed M. Meesum; Fahad Panolan; Saket Saurabh; Meirav Zehavi

doi:10.1137/17M1154370

Rank vertex cover as a natural problem for algebraic compression

Syed M. Meesum, Fahad Panolan, Saket Saurabh, Meirav Zehavi

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

The question of the existence of a polynomial kernelization of the Vertex Cover Above LP problem was a long-standing, notorious open problem in parameterized complexity. Some years ago, the breakthrough work by Kratsch and Wahlström on representative sets finally answered this question in the affirmative [FOCS 2012]. In this paper, we present an alternative, algebraic compression of the Vertex Cover Above LP problem into the Rank Vertex Cover problem. Here, the input consists of a graph G, a parameter k, and a bijection between V(G) and the set of columns of a representation of a matroid M, and the objective is to find a vertex cover whose rank is upper bounded by k.

Original language	English
Pages (from-to)	1277-1296
Number of pages	20
Journal	SIAM Journal on Discrete Mathematics
Volume	33
Issue number	3
DOIs	https://doi.org/10.1137/17M1154370
State	Published - 1 Jan 2019

Keywords

Algebraic compression
Kernelization
Odd cycle transversal
Vertex cover

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1137/17M1154370

Cite this

@article{5ecaa756c4364dc1b4acfc2203dad9fd,

title = "Rank vertex cover as a natural problem for algebraic compression",

abstract = "The question of the existence of a polynomial kernelization of the Vertex Cover Above LP problem was a long-standing, notorious open problem in parameterized complexity. Some years ago, the breakthrough work by Kratsch and Wahlstr{\"o}m on representative sets finally answered this question in the affirmative [FOCS 2012]. In this paper, we present an alternative, algebraic compression of the Vertex Cover Above LP problem into the Rank Vertex Cover problem. Here, the input consists of a graph G, a parameter k, and a bijection between V(G) and the set of columns of a representation of a matroid M, and the objective is to find a vertex cover whose rank is upper bounded by k.",

keywords = "Algebraic compression, Kernelization, Odd cycle transversal, Vertex cover",

author = "Meesum, {Syed M.} and Fahad Panolan and Saket Saurabh and Meirav Zehavi",

note = "Publisher Copyright: {\textcopyright} 2019 Society for Industrial and Applied Mathematics",

year = "2019",

month = jan,

day = "1",

doi = "10.1137/17M1154370",

language = "English",

volume = "33",

pages = "1277--1296",

journal = "SIAM Journal on Discrete Mathematics",

issn = "0895-4801",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "3",

}

TY - JOUR

T1 - Rank vertex cover as a natural problem for algebraic compression

AU - Meesum, Syed M.

AU - Panolan, Fahad

AU - Saurabh, Saket

AU - Zehavi, Meirav

PY - 2019/1/1

Y1 - 2019/1/1

N2 - The question of the existence of a polynomial kernelization of the Vertex Cover Above LP problem was a long-standing, notorious open problem in parameterized complexity. Some years ago, the breakthrough work by Kratsch and Wahlström on representative sets finally answered this question in the affirmative [FOCS 2012]. In this paper, we present an alternative, algebraic compression of the Vertex Cover Above LP problem into the Rank Vertex Cover problem. Here, the input consists of a graph G, a parameter k, and a bijection between V(G) and the set of columns of a representation of a matroid M, and the objective is to find a vertex cover whose rank is upper bounded by k.

AB - The question of the existence of a polynomial kernelization of the Vertex Cover Above LP problem was a long-standing, notorious open problem in parameterized complexity. Some years ago, the breakthrough work by Kratsch and Wahlström on representative sets finally answered this question in the affirmative [FOCS 2012]. In this paper, we present an alternative, algebraic compression of the Vertex Cover Above LP problem into the Rank Vertex Cover problem. Here, the input consists of a graph G, a parameter k, and a bijection between V(G) and the set of columns of a representation of a matroid M, and the objective is to find a vertex cover whose rank is upper bounded by k.

KW - Algebraic compression

KW - Kernelization

KW - Odd cycle transversal

KW - Vertex cover

UR - http://www.scopus.com/inward/record.url?scp=85071514481&partnerID=8YFLogxK

U2 - 10.1137/17M1154370

DO - 10.1137/17M1154370

M3 - Article

AN - SCOPUS:85071514481

SN - 0895-4801

VL - 33

SP - 1277

EP - 1296

JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

IS - 3

ER -

Rank vertex cover as a natural problem for algebraic compression

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this