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Special Issue: Selected Papers from the 19th Annual International Symposium on Algorithms and Computation (ISAAC 2008), 15–17 December 2008, Gold Coast, AustraliaNo Access


    Given a set T of n points in ℝ2, a Manhattan network on T is a graph G = (V,E) with the property that all the edges in E are vertical or horizontal line segments connecting points in V ⊇ T and for all p, q ∈ T, the graph contains a path having the length exactly L1 distance between p and q. The Minimum Manhattan Network problem is to find a Manhattan network of minimum length, i.e. minimizing the total length of the line segments of the network. In this paper we present a 2-approximation algorithm with time complexity O(n log n), which improves over a recent combinatorial 2-approximation algorithm with running time O(n2). Moreover, compared with other 2-approximation algorithms using linear programming or dynamic programming techniques, we show that a greedy strategy suffices to obtain a 2-approximation algorithm.


    • M. Benkert, T. Shirabe and A. Wolff, The minimum Manhattan network problem: A fast factor-3 approximation, Proc. 20th European Workshop on Computational Geometry pp. 209–212. Google Scholar
    • M. Benkertet al., Comput. Geom.: Th. Appl. 35, 188 (2006). Crossref, ISIGoogle Scholar
    • G. Chalmet, L. Francis and A. Kolen, Eur. J. Oper. Res. 6, 117 (1981), DOI: 10.1016/0377-2217(81)90197-1. Crossref, ISIGoogle Scholar
    • V. Chepoi, K. Nouioua and Y. Vaxès, A rounding algorithm for approximating minimum Manhattan networks, Theor. Comput. Sci. 390 (2008) 56–69. Preliminary version appeared in Proc. 8th Int. Workshop on Approximation Algorithms for Combinatorial Optimization, (2005), pp. 40–51 . Google Scholar
    • F. Y. L. Chin, Z. Guo and H. Sun, Minimum Manhattan network is NP-complete, Proc. 25th Ann. ACM Symp. Computational Geometry pp. 393–402. Google Scholar
    • D. Eppstein, Spanning Trees and Spanners, eds. J. Sack and J. Urrutia (Elsevier Science Publishers B. V. North-Holland, Amsterdam, 2000) pp. 425–461. CrossrefGoogle Scholar
    • B. Fuchs and A. Schulze, A simple 3-approximation of minimum Manhattan networks, Proc. 7th Cologne Twente Workshop on Graphs and Combinatorial Optimization pp. 26–29. Google Scholar
    • J. Gudmundsson, C. Levcopoulos and G. Narasimhan, Approximating a minimum Manhattan network, Nord. J. Computing 8 (2001) 219–232. Preliminary version appeared in Proc. 2nd Int. Workshop on Approximation Algorithms for Combinatorial Optimization, (1999), pp. 28–37 . Google Scholar
    • J. Gudmundssonet al., Small Manhattan networks and algorithms for the Earth Mover's distance, Proc. 23rd European Workshop on Computational Geometry pp. 174–177. Google Scholar
    • Z. Guo, H. Sun and H. Zhu, A fast 2-approximation algorithm for the minimum Manhattan network problem, Proc. 4th Int. Conf. Algorithmic Aspects in Information and Management5034, Lecture Notes in Computer Science (Springer-Verlag, 2008) pp. 212–223. Google Scholar
    • R. Kato, K. Imai and T. Asano, An improved algorithm for the minimum Manhattan network problem, Proc. 13th Int. Symp. Algorithms and Computation2518, Lecture Notes in Computer Science (Springer-Verlag, 2002) pp. 344–356. Google Scholar
    • F. Lam, M. Alexandersson and L. Pachter, J. Comput. Biol. 10, 509 (2003), DOI: 10.1089/10665270360688156. Crossref, ISIGoogle Scholar
    • X. Muñoz, S. Seibert and W. Unger, The minimal Manhattan network problem in three dimensions, Proc. 3rd Int. Workshop on Algorithms and Computation5431, Lecture Notes in Computer Science (Springer-Verlag, 2009) pp. 369–380. Google Scholar
    • K. Nouioua, Enveloppes de Pareto et Réseaux de Manhattan: Caractérisations et algorithmes, Ph.D. thesis, Université de la Méditerranée, 2005 . Google Scholar
    • S. Seibert and W. Unger, A 1.5-approximation of the minimal Manhattan network problem, Proc. 16th Int. Symp. Algorithms and Computation3827, Lecture Notes in Computer Science (Springer-Verlag, 2005) pp. 246–255. Google Scholar
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