Analysis of Lagrangian lower bounds for a graph partitioning problem

Date

1999

Authors

Adil, G. K.
Ghosh, J. B.

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Source Title

Operations Research

Print ISSN

0030-364X

Electronic ISSN

1526-5463

Publisher

Institute for Operations Research and the Management Sciences (INFORMS)

Volume

47

Issue

5

Pages

785 - 788

Language

English

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Abstract

Recently, Ahmadi and Tang (1991) demonstrated how various manufacturing problems can be modeled and solved as graph partitioning problems. They use Lagrangian relaxation of two different mixed integer programming formulations to obtain both heuristic solutions and lower bounds on optimal solution values. In this note, we point to certain inconsistencies in the reported results. Among other things, we show analytically that the first bound proposed is trivial (i.e., it can never have a value greater than zero) while the second is also trivial for certain sparse graphs. We also present limited empirical results on the behavior of this second bound as a function of graph density.

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Published Version (Please cite this version)