Enumerating Constrained Non-crossing Geometric Spanning Trees

  • Naoki Katoh
  • Shin-ichi Tanigawa
Conference paper

DOI: 10.1007/978-3-540-73545-8_25

Part of the Lecture Notes in Computer Science book series (LNCS, volume 4598)
Cite this paper as:
Katoh N., Tanigawa S. (2007) Enumerating Constrained Non-crossing Geometric Spanning Trees. In: Lin G. (eds) Computing and Combinatorics. COCOON 2007. Lecture Notes in Computer Science, vol 4598. Springer, Berlin, Heidelberg

Abstract

In this paper we present an algorithm for enumerating without repetitions all non-crossing geometric spanning trees on a given set of n points in the plane under edge inclusion constraints (i.e., some edges are required to be included in spanning trees). We will first prove that a set of all edge-constrained non-crossing spanning trees is connected via remove-add flips, based on the constrained smallest indexed triangulation which is obtained by extending the lexicographically ordered triangulation introduced by Bespamyatnikh. More specifically, we prove that all edge-constrained triangulations can be transformed to the smallest indexed triangulation among them by O(n2) times of greedy flips. Our enumeration algorithm generates each output graph in O(n2) time and O(n) space based on reverse search technique.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Naoki Katoh
    • 1
  • Shin-ichi Tanigawa
    • 1
  1. 1.Department of Architecture and Architectural Engineering, Kyoto University, Kyoto 615-8450Japan

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