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

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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