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Workshop on Algorithms and Data Structures

WADS 1997: Algorithms and Data Structures pp 234–247Cite as

An efficient algorithm for shortest paths in vertical and horizontal segments

  • Session 8A: Invited Lecture
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1272))

Abstract

Suppose one has a line segment arrangement consisting entirely of vertical and horizontal segments, and one wants to find the shortest path from one point to another along these segments. Using known algorithms one can solve this in O(n 2) time and in O(n 2) space. We show that it is possible to find a shortest path in time O(n1.5 log n) and space O(n 1.5). Furthermore, if only one path endpoint is known in advance, it is possible to preprocess the arrangement in the same time and space and then find shortest paths for query points in time O(log n).

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Author information

Authors and Affiliations

  1. Department of Information and Computer Science, University of California, 92697-3425, Irvine, CA

    David Eppstein & David W. Hart

Authors
  1. David Eppstein
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  2. David W. Hart
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Editor information

Frank Dehne Andrew Rau-Chaplin Jörg-Rüdiger Sack Roberto Tamassia

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© 1997 Springer-Verlag Berlin Heidelberg

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Eppstein, D., Hart, D.W. (1997). An efficient algorithm for shortest paths in vertical and horizontal segments. In: Dehne, F., Rau-Chaplin, A., Sack, JR., Tamassia, R. (eds) Algorithms and Data Structures. WADS 1997. Lecture Notes in Computer Science, vol 1272. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63307-3_63

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  • DOI: https://doi.org/10.1007/3-540-63307-3_63

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63307-5

  • Online ISBN: 978-3-540-69422-9

  • eBook Packages: Springer Book Archive

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