Approximation Algorithms for Min-Max Tree Partition

Nili Guttmann-Beck*, Refael Hassin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the problem of partitioning the node set of a graph into p equal sized subsets. The objective is to minimize the maximum length, over these subsets, of a minimum spanning tree. We show that no polynomial algorithm with bounded error ratio can be given for the problem unless P = NP. We present an O(n2) time algorithm for the problem, where n is the number of nodes in the graph. Assuming that the edge lengths satisfy the triangle inequality, its error ratio is at most 2p -1. We also present an improved algorithm that obtains as an input a positive integer x. It runs in O(2(p+x)pn2) time, and its error ratio is at most (2 -x/ (x + p - 1))p.

Original languageEnglish
Pages (from-to)266-286
Number of pages21
JournalJournal of Algorithms
Volume24
Issue number2
DOIs
StatePublished - Aug 1997

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