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Efficient Algorithms for Disjoint Matchings among Intervals and Related Problems

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Discrete Mathematics and Theoretical Computer Science (DMTCS 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2731))

Abstract

In this note, the problem of determining disjoint matchings in a set of intervals is investigated (two intervals can be matched if they are disjoint). Such problems find applications in schedules planning. First, we propose a new incremental algorithm to compute maximum disjoint matchings among intervals. We show that this algorithm runs in O(n) time if the intervals are given ordered in input. Additionally, a shorter algorithm is given for the case where the intervals are proper. Then, a NP-complete extension of this problem is considered: the perfect disjoint multidimensional matching problem among intervals. A sufficient condition is established for the existence of such a matching. The proof of this result yields a linear-time algorithm to compute it in this case. Besides, a greedy heuristic is shown to solve the problem in linear time for proper intervals.

The author works under contract with the firm Prologia-Groupe Air Liquide.

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Authors and Affiliations

  1. Laboratoire d’Informatique Fondamentale, Parc Scientifique et Technologique de Luminy, Case 901 - 163, Avenue de Luminy, 13288, Marseille Cedex 9, France

    Frédéric Gardi

Authors
  1. Frédéric Gardi
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Auckland, Maths-Physics Building 303, 38 Princes St., Auckland, New Zealand

    Cristian S. Calude  & Michael J. Dinneen  & 

  2. Université de Bourgogne, LE2I, B.P. 47870, 21078, Dijon Cedex, France

    Vincent Vajnovszki

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© 2003 Springer-Verlag Berlin Heidelberg

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Gardi, F. (2003). Efficient Algorithms for Disjoint Matchings among Intervals and Related Problems. In: Calude, C.S., Dinneen, M.J., Vajnovszki, V. (eds) Discrete Mathematics and Theoretical Computer Science. DMTCS 2003. Lecture Notes in Computer Science, vol 2731. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45066-1_13

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  • DOI: https://doi.org/10.1007/3-540-45066-1_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40505-4

  • Online ISBN: 978-3-540-45066-5

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