Skip to main content
SpringerLink
Log in

Maximum Independent Set in 2-Direction Outersegment Graphs

  • Conference paper
Graph-Theoretic Concepts in Computer Science (WG 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6986))

Included in the following conference series:

  • 800 Accesses

Abstract

An outersegment graph is the intersection graph of line-segments lying inside a disk and having one end-point on the boundary of the disk. We present a polynomial-time algorithm for the problem of computing a maximum independent set in outersegment graphs where every segment is either horizontally or vertically aligned. We assume that a geometric representation of the graph is given as input.

This work was partially funded by the Swiss National Science Foundation (SNF grant no. 200021-125033/1).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Brandstädt, A., Le, V.B., Spinrad, J.P.: Graph classes: a survey. SIAM Monographs on Discrete Mathematics and Applications. Society for Industrial and Applied Mathematics Mathematics (1999)

    Google Scholar 

  2. Flier, H., Mihalák, M., Schöbel, A., Widmayer, P., Zych, A.: Vertex Disjoint Paths for Dispatching in Railways. In: Proceedings of the 10th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS), Schloss Dagstuhl–Leibniz-Zentrum für Informatik, vol. 14, pp. 61–73 (2010)

    Google Scholar 

  3. Fox, J., Pach, J.: Coloring K k -free intersection graphs of geometric objects in the plane. In: Proceedings of the 24th ACM Symposium on Computational Geometry (SoCG), pp. 346–354. ACM (2008)

    Google Scholar 

  4. Fox, J., Pach, J.: Erdős-Hajnal-type results on intersection patterns of geometric objects. In: Győri, E., Katona, G.O.H., Lovász, L. (eds.) Horizons of Combinatorics, vol. 17, pp. 79–103. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  5. Fox, J., Pach, J.: A separator theorem for string graphs and its applications. Combinatorics, Probability and Computing 19(03), 371–390 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  6. Gavril, F.: Maximum weight independent sets and cliques in intersection graphs of filaments. Information Processing Letters 73(5-6), 181–188 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  7. Mark Keil, J.: The complexity of domination problems in circle graphs. Discrete Applied Mathematics 42(1), 51–63 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  8. Kratochvíl, J.: String graphs. I. The number of critical nonstring graphs is infinite. Journal of Combinatorial Theory, Series B 52(1), 53–66 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kratochvíl, J.: String graphs. II. Recognizing string graphs is NP-hard. Journal of Combinatorial Theory, Series B 52(1), 67–78 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  10. Kratochvíl, J., Matoušek, J.: String graphs requiring exponential representations. Journal of Combinatorial Theory, Series B 53(1), 1–4 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  11. Kratochvíl, J., Nešetřil, J.: INDEPENDENT SET and CLIQUE problems in intersection-defined classes of graphs. Commentationes Mathematicae Universitatis Carolinae 31(1), 85–93 (1990)

    MathSciNet  MATH  Google Scholar 

  12. Middendorf, M., Pfeiffer, F.: The max clique problem in classes of string-graphs. Discrete Mathematics 108(1-3), 365–372 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  13. Pach, J., Tóth, G.: Recognizing string graphs is decidable. Discrete & Computational Geometry 28, 593–606 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  14. Schaefer, M., Sedgwick, E., Štefankovič, D.: Recognizing string graphs in NP. Journal of Computer and System Sciences 67(2), 365–380 (2003); Special Issue on STOC 2002

    Article  MathSciNet  MATH  Google Scholar 

  15. Schrijver, A.: Combinatorial Optimization: Polyhedra and Efficiency. Springer, Heidelberg (2003)

    MATH  Google Scholar 

  16. Unger, W.: On the k-colouring of circle-graphs. In: Cori, R., Wirsing, M. (eds.) STACS 1988. LNCS, vol. 294, pp. 61–72. Springer, Heidelberg (1988)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Theoretical Computer Science, ETH Zürich, Switzerland

    Holger Flier, Matúš Mihalák, Peter Widmayer & Anna Zych

Authors
  1. Holger Flier
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Matúš Mihalák
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Peter Widmayer
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Anna Zych
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. KAM MFF UK, Charles University, Malostranské nám 25, 11800, Praha 1, Czech Republic

    Petr Kolman  & Jan Kratochvíl  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Flier, H., Mihalák, M., Widmayer, P., Zych, A. (2011). Maximum Independent Set in 2-Direction Outersegment Graphs. In: Kolman, P., Kratochvíl, J. (eds) Graph-Theoretic Concepts in Computer Science. WG 2011. Lecture Notes in Computer Science, vol 6986. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25870-1_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-25870-1_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25869-5

  • Online ISBN: 978-3-642-25870-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation