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

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.