A greedy heuristic for a minimum-weight forest problem

Authors:
Celina Imieliska;Bahman Kalantari;Leonid Khachiyan
Affiliations:
Department of Electrical Engineering and Computer Science, Stevens Institute of Technology, Hoboken, NJ 07030, USA;Departments of Computer Science, Rutgers University, New Brunswick, NJ 08903, USA;Departments of Computer Science, Rutgers University, New Brunswick, NJ 08903, USA
Venue:
Operations Research Letters
Year:
1993

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Abstract

Given an undirected edge-weighted graph and a natural number m, we consider the problem of finding a minimum-weight spanning forest such that each of its trees spans at least m vertices. For m = 4, the problem is shown to the NP-hard. We describe a simple 2-approximate greedy heuristic that runs within the time needed to compute a minimum spanning tree. If the edge weights satisfy the triangle inequality, any such a 2-approximate solution, in linear time, can be converted into a 4-approximate solution for the problem of covering the graph with minimum-weight vertex disjoint cycles of size at least m.