A local search 4/3-approximation algorithm for the minimum 3-path partition problem

Yong Chen; Randy Goebel; Guohui Lin; Longcheng Liu; Bing Su; Weitian Tong; Yao Xu; An Zhang

doi:10.1007/s10878-022-00915-5

A local search 4/3-approximation algorithm for the minimum 3-path partition problem

Yong Chen, Randy Goebel, Guohui Lin, Longcheng Liu, Bing Su, Weitian Tong, Yao Xu, An Zhang

Computer Science

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

2 Scopus citations

Abstract

Given a graph G= (V, E) , the 3-path partition problem is to find a minimum collection of vertex-disjoint paths each of order at most 3 to cover all the vertices of V. The previous best approximation algorithm for the 3-path partition problem has a performance ratio 13/9, which is based on a simple local search strategy. We propose a more involved local search and show by an amortized analysis that it is a 4/3-approximation; we also design an instance to illustrate that the approximation ratio is tight.

Original language	English
Pages (from-to)	3595-3610
Number of pages	16
Journal	Journal of Combinatorial Optimization
Volume	44
Issue number	5
DOIs	https://doi.org/10.1007/s10878-022-00915-5
State	Published - Dec 2022

Scopus Subject Areas

Computer Science Applications
Discrete Mathematics and Combinatorics
Control and Optimization
Computational Theory and Mathematics
Applied Mathematics

Keywords

Amortized analysis
Approximation algorithms
Local search
Path cover
Path partition

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10.1007/s10878-022-00915-5

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abstract = "Given a graph G= (V, E) , the 3-path partition problem is to find a minimum collection of vertex-disjoint paths each of order at most 3 to cover all the vertices of V. The previous best approximation algorithm for the 3-path partition problem has a performance ratio 13/9, which is based on a simple local search strategy. We propose a more involved local search and show by an amortized analysis that it is a 4/3-approximation; we also design an instance to illustrate that the approximation ratio is tight.",

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AU - Goebel, Randy

AU - Lin, Guohui

AU - Liu, Longcheng

AU - Su, Bing

AU - Tong, Weitian

AU - Xu, Yao

AU - Zhang, An

PY - 2022/12

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AB - Given a graph G= (V, E) , the 3-path partition problem is to find a minimum collection of vertex-disjoint paths each of order at most 3 to cover all the vertices of V. The previous best approximation algorithm for the 3-path partition problem has a performance ratio 13/9, which is based on a simple local search strategy. We propose a more involved local search and show by an amortized analysis that it is a 4/3-approximation; we also design an instance to illustrate that the approximation ratio is tight.

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KW - Approximation algorithms

KW - Local search

KW - Path cover

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A local search 4/3-approximation algorithm for the minimum 3-path partition problem

Abstract

Scopus Subject Areas

Keywords

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