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arXiv · 1812.09353

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
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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 $V$. 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.

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Yong Chen, Randy Goebel, Guohui Lin, Longcheng Liu, Bing Su, Weitian Tong, Yao Xu, An Zhang. 2018-12-21. A local search $4/3$-approximation algorithm for the minimum $3$-path partition problem. https://arxiv.org/abs/1812.09353

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