A Fast 2-Approximation Algorithm for the Minimum Manhattan Network Problem

Authors:
Zeyu Guo;He Sun;Hong Zhu
Affiliations:
Department of Computer Science and Engineering, Fudan University, China;Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, China;Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, China
Venue:
AAIM '08 Proceedings of the 4th international conference on Algorithmic Aspects in Information and Management
Year:
2008

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Abstract

Given a set Tof npoints in 驴2, a Manhattan Network Gis a network with all its edges horizontal or vertical segments, such that for all p,q驴 T, in Gthere exists a path (named a Manhattan path) of the length exactly the Manhattan distance between pand q. The Minimum Manhattan Network (MMN) problem is to find a Manhattan network of the minimum length, i.e., the total length of the segments of the network is to be minimized. In this paper we present a 2-approximation algorithm with time complexity O(n2), which improves the 2-approximation algorithm with time complexity 驴(n8), proposed by Chepoi, Nouioua et al.. To the best of our knowledge, this is the best result on this problem.