A probabilistic algorithm for vertex cover

D. Berend; S. Mamana

doi:10.1016/j.tcs.2023.114306

A probabilistic algorithm for vertex cover

D. Berend, S. Mamana

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

1 Scopus citations

Abstract

The Minimum Vertex CoverProblem is the optimization problem of finding a vertex cover V_c of minimal cardinality in a given graph. It is a classic NP-hard problem, and various algorithms have been suggested for it. In this paper, we start with a basic algorithm for solving the problem. Using a probabilistic idea, we use it to develop an improved algorithm. The algorithm is greedy; at each step it adds to the cover a vertex such that the expected cover size, if we continue randomly after this step, is minimal. We study the new algorithm theoretically and empirically, and run simulations to compare its performance to that of some algorithms of a similar nature.

Original language	English
Article number	114306
Journal	Theoretical Computer Science
Volume	983
DOIs	https://doi.org/10.1016/j.tcs.2023.114306
State	Published - 1 Feb 2024

Keywords

Algorithm
Derandomization
Random graph
Vertex cover

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1016/j.tcs.2023.114306

Cite this

@article{cf33c88271f84035b8b72025bce1b1a6,

title = "A probabilistic algorithm for vertex cover",

abstract = "The Minimum Vertex CoverProblem is the optimization problem of finding a vertex cover Vc of minimal cardinality in a given graph. It is a classic NP-hard problem, and various algorithms have been suggested for it. In this paper, we start with a basic algorithm for solving the problem. Using a probabilistic idea, we use it to develop an improved algorithm. The algorithm is greedy; at each step it adds to the cover a vertex such that the expected cover size, if we continue randomly after this step, is minimal. We study the new algorithm theoretically and empirically, and run simulations to compare its performance to that of some algorithms of a similar nature.",

keywords = "Algorithm, Derandomization, Random graph, Vertex cover",

author = "D. Berend and S. Mamana",

note = "Publisher Copyright: {\textcopyright} 2023 Elsevier B.V.",

year = "2024",

month = feb,

day = "1",

doi = "10.1016/j.tcs.2023.114306",

language = "English",

volume = "983",

journal = "Theoretical Computer Science",

issn = "0304-3975",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - A probabilistic algorithm for vertex cover

AU - Berend, D.

AU - Mamana, S.

PY - 2024/2/1

Y1 - 2024/2/1

N2 - The Minimum Vertex CoverProblem is the optimization problem of finding a vertex cover Vc of minimal cardinality in a given graph. It is a classic NP-hard problem, and various algorithms have been suggested for it. In this paper, we start with a basic algorithm for solving the problem. Using a probabilistic idea, we use it to develop an improved algorithm. The algorithm is greedy; at each step it adds to the cover a vertex such that the expected cover size, if we continue randomly after this step, is minimal. We study the new algorithm theoretically and empirically, and run simulations to compare its performance to that of some algorithms of a similar nature.

AB - The Minimum Vertex CoverProblem is the optimization problem of finding a vertex cover Vc of minimal cardinality in a given graph. It is a classic NP-hard problem, and various algorithms have been suggested for it. In this paper, we start with a basic algorithm for solving the problem. Using a probabilistic idea, we use it to develop an improved algorithm. The algorithm is greedy; at each step it adds to the cover a vertex such that the expected cover size, if we continue randomly after this step, is minimal. We study the new algorithm theoretically and empirically, and run simulations to compare its performance to that of some algorithms of a similar nature.

KW - Algorithm

KW - Derandomization

KW - Random graph

KW - Vertex cover

UR - http://www.scopus.com/inward/record.url?scp=85177548410&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2023.114306

DO - 10.1016/j.tcs.2023.114306

M3 - Article

AN - SCOPUS:85177548410

SN - 0304-3975

VL - 983

JO - Theoretical Computer Science

JF - Theoretical Computer Science

M1 - 114306

ER -

A probabilistic algorithm for vertex cover

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this