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International Workshop on Combinatorial Image Analysis

IWCIA 2017: Combinatorial Image Analysis pp 30–39Cite as

On Sets of Line Segments Featuring a Cactus Structure

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Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10256))

Abstract

In this paper we derive sharp upper and lower bounds on the number of intersections and closed regions that can occur in a set of line segments whose underlying planar graph is a cactus graph. These bounds can be used to evaluate the complexity of certain algorithms for problems defined on sets of segments in terms of the cardinality of the segment sets. In particular, we give an application in the problem of finding a path between two points in a set of segments which travels through a minimum number of segments.

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Acknowledgements

We thank the three anonymous reviewers for their valuable comments. This material is based upon work supported by the National Science Foundation under Grant No. 1450681.

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Authors and Affiliations

  1. Computational and Applied Mathematics, Rice University, Houston, TX, 77005, USA

    Boris Brimkov

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  1. Boris Brimkov
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Correspondence to Boris Brimkov .

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Editors and Affiliations

  1. SUNY Buffalo State, Buffalo, New York, USA

    Valentin E. Brimkov

  2. Department of Applied Professional Studies, SUNY Fredonia, Fredonia, New York, USA

    Reneta P. Barneva

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Brimkov, B. (2017). On Sets of Line Segments Featuring a Cactus Structure. In: Brimkov, V., Barneva, R. (eds) Combinatorial Image Analysis. IWCIA 2017. Lecture Notes in Computer Science(), vol 10256. Springer, Cham. https://doi.org/10.1007/978-3-319-59108-7_3

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  • DOI: https://doi.org/10.1007/978-3-319-59108-7_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59107-0

  • Online ISBN: 978-3-319-59108-7

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