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The Minimum Latency Problem Is NP-Hard for Weighted Trees

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Integer Programming and Combinatorial Optimization (IPCO 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2337))

Abstract

In the minimum latency problem (MLP) we are given n points v 1,..., v n and a distance d(v i,v j) between any pair of points. We have to find a tour, starting at v 1 and visiting all points, for which the sum of arrival times is minimal. The arrival time at a point v i is the traveled distance from v 1 to v i in the tour. The minimum latency problem is MAX-SNP-hard for general metric spaces, but the complexity for the problem where the metric is given by an edge-weighted tree has been a long-standing open problem. We show that the minimum latency problem is NP-hard for trees even with weights in {0,1}.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, P.O.Box 513, 5600 MB, Eindhoven, The Netherlands

    René Sitters

Authors
  1. René Sitters
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Editor information

Editors and Affiliations

  1. Program in Applied and Computational Mathematics, University of Princeton, Fine Hall, Washington Road, Princeton, NJ, 08544-1000, USA

    William J. Cook

  2. Sloan School of Management, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139-4307, USA

    Andreas S. Schulz

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© 2002 Springer-Verlag Berlin Heidelberg

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Sitters, R. (2002). The Minimum Latency Problem Is NP-Hard for Weighted Trees. In: Cook, W.J., Schulz, A.S. (eds) Integer Programming and Combinatorial Optimization. IPCO 2002. Lecture Notes in Computer Science, vol 2337. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47867-1_17

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  • DOI: https://doi.org/10.1007/3-540-47867-1_17

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43676-8

  • Online ISBN: 978-3-540-47867-6

  • eBook Packages: Springer Book Archive

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