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

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

Data Structures and Algorithms 2018-12-27 v1

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

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 $V$ . It is different from but closely related to the well-known $3$ -set cover problem. The best known approximation algorithm for the $3$ -path partition problem was proposed recently and has a ratio $13/9$ . Here we present a local search algorithm and show, by an amortized analysis, that it is a $4/3$ -approximation. This ratio matches up to the best approximation ratio for the $3$ -set cover problem.

Keywords

shortest path problem approximation algorithm path planning

Cite

@article{arxiv.1812.09353,
  title  = {A local search $4/3$-approximation algorithm for the minimum $3$-path partition problem},
  author = {Yong Chen and Randy Goebel and Guohui Lin and Longcheng Liu and Bing Su and Weitian Tong and Yao Xu and An Zhang},
  journal= {arXiv preprint arXiv:1812.09353},
  year   = {2018}
}

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16 pages, 21 figures

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

Abstract

Keywords

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