The bottleneck k-MST

Authors:
Abraham P. Punnen;Olena Chapovska
Affiliations:
Department of Mathematics, Simon Fraser University, Surrey, British Columbia, Canada and University of New Brunswick, Saint John;Department of Mathematical Sciences, University of New Brunswick, Saint John, Canada
Venue:
Information Processing Letters
Year:
2005

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Abstract

The k-MST is a well known NP-hard problem and several approximation algorithms exist to solve this problem with a guaranteed performance bound. A closely related problem, called the bottleneck k-MST (BMST(k)) can however be solved in O(m log n) time on graph with n nodes and m edges. We propose two algorithms to solve BMST(k), one of complexity O(m + n log n) and the other of O(m) time. We also consider a generalization of BMST(k) which subsumes many bottleneck problems studied in the literature and show that this generalized problem can also be solved in O(m) time.