A greedy approximation algorithm for the uniform metric labeling problem analyzed by a primal-dual technique

Authors:
Evandro C. Bracht;Luis A. A. Meira;F. K. Miyazawa
Affiliations:
Universidade Estadual de Campinas, Campinas--SP, Brazil;Universidade Estadual de Campinas, Campinas--SP, Brazil;Universidade Estadual de Campinas, Campinas--SP, Brazil
Venue:
Journal of Experimental Algorithmics (JEA)
Year:
2005

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Abstract

We consider the uniform metric labeling problem. This NP-hard problem considers how to assign objects to labels respecting assignment and separation costs. The known approximation algorithms are based on solutions of large linear programs and are impractical for moderate- and large-size instances. We present an 8log n-approximation algorithm that can be applied to large-size instances. The algorithm is greedy and is analyzed by a primal-dual technique. We implemented the presented algorithm and two known approximation algorithms and compared them at randomized instances. The gain of time was considerable with small error ratios. We also show that the analysis is tight, up to a constant factor.