An Efficient Polynomial Time Approximation Scheme for the Vertex Cover P3 Problem on Planar Graphs

An Efficient Polynomial Time Approximation Scheme for the Vertex Cover P3 Problem on Planar Graphs

Given a graph G = (V,E), the task in the vertex cover P3(V C P3) problem is to find a minimum subset of vertices F ⊆ V such that every path of order 3 in G contains at least one vertex from F. The V C P3problem remains NP-hard even in planar graphs and has many applications in real world. In this pa...

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Bibliographic Details
Main Authors: Tu Jianhua, Shi Yongtang
Format: Article
Language:English
Published: Sciendo 2019-02-01
Series:Discussiones Mathematicae Graph Theory
Subjects:
combinatorial optimization
vertex cover p3 problem
branch- width
planar graphs
eptas
05c85
Online Access:https://doi.org/10.7151/dmgt.2060
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spelling doaj-5b4b067dae5c4fe2a229b36524eccdb72021-09-05T17:20:23ZengSciendoDiscussiones Mathematicae Graph Theory2083-58922019-02-01391556510.7151/dmgt.2060dmgt.2060An Efficient Polynomial Time Approximation Scheme for the Vertex Cover P3 Problem on Planar GraphsTu Jianhua0Shi Yongtang1School of Science Beijing University of Chemical TechnologyBeijing, ChinaCenter for Combinatorics and LPMC Nankai UniversityTianjin, ChinaGiven a graph G = (V,E), the task in the vertex cover P3(V C P3) problem is to find a minimum subset of vertices F ⊆ V such that every path of order 3 in G contains at least one vertex from F. The V C P3problem remains NP-hard even in planar graphs and has many applications in real world. In this paper, we give a dynamic-programming algorithm to solve the V C P3problem on graphs of bounded branchwidth. Using the dynamic programming algorithm and the Baker’s EPTAS framework for NP-hard problems, we present an efficient polynomial time approximation scheme (EPTAS) for the V C P3problem on planar graphs.https://doi.org/10.7151/dmgt.2060combinatorial optimizationvertex cover p3 problembranch- widthplanar graphseptas05c85
collection DOAJ
language English
format Article
sources DOAJ
author Tu Jianhua
Shi Yongtang
spellingShingle Tu Jianhua
Shi Yongtang
An Efficient Polynomial Time Approximation Scheme for the Vertex Cover P3 Problem on Planar Graphs
Discussiones Mathematicae Graph Theory
combinatorial optimization
vertex cover p3 problem
branch- width
planar graphs
eptas
05c85
author_facet Tu Jianhua
Shi Yongtang
author_sort Tu Jianhua
title An Efficient Polynomial Time Approximation Scheme for the Vertex Cover P3 Problem on Planar Graphs
title_short An Efficient Polynomial Time Approximation Scheme for the Vertex Cover P3 Problem on Planar Graphs
title_full An Efficient Polynomial Time Approximation Scheme for the Vertex Cover P3 Problem on Planar Graphs
title_fullStr An Efficient Polynomial Time Approximation Scheme for the Vertex Cover P3 Problem on Planar Graphs
title_full_unstemmed An Efficient Polynomial Time Approximation Scheme for the Vertex Cover P3 Problem on Planar Graphs
title_sort efficient polynomial time approximation scheme for the vertex cover p3 problem on planar graphs
publisher Sciendo
series Discussiones Mathematicae Graph Theory
issn 2083-5892
publishDate 2019-02-01
description Given a graph G = (V,E), the task in the vertex cover P3(V C P3) problem is to find a minimum subset of vertices F ⊆ V such that every path of order 3 in G contains at least one vertex from F. The V C P3problem remains NP-hard even in planar graphs and has many applications in real world. In this paper, we give a dynamic-programming algorithm to solve the V C P3problem on graphs of bounded branchwidth. Using the dynamic programming algorithm and the Baker’s EPTAS framework for NP-hard problems, we present an efficient polynomial time approximation scheme (EPTAS) for the V C P3problem on planar graphs.
topic combinatorial optimization
vertex cover p3 problem
branch- width
planar graphs
eptas
05c85
url https://doi.org/10.7151/dmgt.2060
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