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 () and An Zhang ()
Additional contact information
Yong Chen: Hangzhou Dianzi University
Randy Goebel: University of Alberta
Guohui Lin: University of Alberta
Longcheng Liu: Xiamen University
Bing Su: Xi’an Technological University
Weitian Tong: Georgia Southern University
Yao Xu: Georgia Southern University
An Zhang: Hangzhou Dianzi University

Journal of Combinatorial Optimization, 2022, vol. 44, issue 5, No 20, 3595-3610

Abstract: Abstract Given a graph $$G = (V, E)$$ 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.

Keywords: Path partition; Path cover; Local search; Approximation algorithms; Amortized analysis (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10878-022-00915-5

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