TY - JOUR

T1 - Approximation Algorithms for Min-Max Tree Partition

AU - Guttmann-Beck, Nili

AU - Hassin, Refael

PY - 1997/8

Y1 - 1997/8

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0041969569&partnerID=8YFLogxK

U2 - 10.1006/jagm.1996.0848

DO - 10.1006/jagm.1996.0848

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AN - SCOPUS:0041969569

SN - 0196-6774

VL - 24

SP - 266

EP - 286

JO - Journal of Algorithms

JF - Journal of Algorithms

IS - 2

ER -