A rounding algorithm for approximating minimum manhattan networks

Authors:
Victor Chepoi;Karim Nouioua;Yann Vaxès
Affiliations:
Laboratoire d'Informatique Fondamentale de Marseille, Faculté des Sciences de Luminy, Universitée de la Méditerranée, Marseille Cedex 9, France;Laboratoire d'Informatique Fondamentale de Marseille, Faculté des Sciences de Luminy, Universitée de la Méditerranée, Marseille Cedex 9, France;Laboratoire d'Informatique Fondamentale de Marseille, Faculté des Sciences de Luminy, Universitée de la Méditerranée, Marseille Cedex 9, France
Venue:
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Year:
2005

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Abstract

For a set T of n points (terminals) in the plane, a Manhattan network on T is a network N(T)=(V,E) with the property that its edges are horizontal or vertical segments connecting points in V⊇T and for every pair of terminals, the network N(T) contains a shortest l1-path between them. A minimum Manhattan network on T is a Manhattan network of minimum possible length. The problem of finding minimum Manhattan networks has been introduced by Gudmundsson, Levcopoulos, and Narasimhan (APPROX'99) and it is not known whether this problem is in P or not. Several approximation algorithms (with factors 8,4, and 3) have been proposed; recently Kato, Imai, and Asano (ISAAC'02) have given a factor 2 approximation algorithm, however their correctness proof is incomplete. In this note, we propose a rounding 2-approximation algorithm based on a LP-formulation of the minimum Manhattan network problem.