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Gray Codes for AT-Free Orders via Antimatroids

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Combinatorial Algorithms (IWOCA 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9538))

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Abstract

The \({{\mathrm{\mathrm {AT}}}}\)-free order is a linear order of the vertices of a graph the existence of which characterizes \({{\mathrm{\mathrm {AT}}}}\)-free graphs. We show that all \({{\mathrm{\mathrm {AT}}}}\)-free orders of an \({{\mathrm{\mathrm {AT}}}}\)-free graph can be generated in O(1) amortized time.

T. Kloks—This author thanks the institute for their hospitality and support.

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Notes

  1. 1.

    A convexity space has Carathéodory number k if k is the smallest integer satisfying the following property. If \(x \in \sigma (X)\) for a set X then there exists a \(X^{\prime } \subseteq X\) with \(|X^{\prime }| \le k\) and \(x \in \sigma (X^{\prime })\).

References

  1. Björner, A., Ziegler, G.: 8 Introduction to greeds. In: White, N. (ed.) Matroid Applications - Encyclopedia of Mathematics and its Applications, vol. 40, pp. 284–357. Cambridge University Press, Cambridge (1992)

    Google Scholar 

  2. Calder, J.: Some elementary properties of interval convexities. J. Lond. Math. Soc. 3, 422–428 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chandran, L., Ibarra, L., Ruskey, F., Sawada, J.: Generating and characterizing the perfect elimination orderings of a chordal graph. Theor. Comput. Sci. 307, 303–317 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  4. Chang, J.-M., Ho, C.-W., Ko, M.-T.: LexBFS-ordering in asteroidal triple-free graphs. In: Aggarwal, A.K., Pandu Rangan, C. (eds.) ISAAC 1999. LNCS, vol. 1741, pp. 163–172. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  5. Chvátal, V.: Antimatroids, betweenness, convexity. In: Cook, W., Lovász, L., Vygen, J. (eds.) Research Trends in Combinatorial Optimization. Bonn, 2009, pp. 57–64. Springer, Heidelberg (2008)

    Google Scholar 

  6. Corneil, D., Stacho, J.: Vertex ordering characterizations of graphs of bounded asteroidal number. J. Graph Theor. 78, 61–79 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  7. Kloks, T., Kratsch, D., Müller, H.: Asteroidal sets in graphs. In: Möhring, Rolf H. (ed.) WG 1997. LNCS, vol. 1335, pp. 229–241. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  8. Kloks, T., Wang, Y.: Advances in graph algorithms. Manuscript viXra:1409.0165 (2014)

  9. Pruesse, G., Ruskey, F.: Gray codes from antimatroids. Order 10(3), 239–252 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  10. Pruesse, G., Ruskey, F.: Generating linear extensions fast. SIAM J. Comput. 23, 373–386 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  11. Sawada, J.: Oracles for vertex elimination orderings. Theor. Comput. Sci. 341, 73–90 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  12. Walter, J.: Representations of chordal graphs as subtrees of a tree. J. Graph Theor. 2, 265–267 (1978)

    Article  MATH  Google Scholar 

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Acknowledgments

The authors would like to thank the anonymous reviewers for the comments. Jou-Ming Chang was supported in part by the MOST grant 104-2221-E-114-002-MY3. Hung-Lung Wang was supported in part by the MOST grant 104-2221-E-114-003.

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Authors and Affiliations

  1. Institute of Information and Decision Sciences, National Taipei University of Business, Taipei, Taiwan

    Jou-Ming Chang, Ton Kloks & Hung-Lung Wang

Authors
  1. Jou-Ming Chang
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  2. Ton Kloks
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  3. Hung-Lung Wang
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Corresponding author

Correspondence to Hung-Lung Wang .

Editor information

Editors and Affiliations

  1. Dept. of Computer Science, University of Verona, Verona, Italy

    Zsuzsanna Lipták

  2. Dept. of Computing and Software, McMaster University, Hamilton, Canada

    William F. Smyth

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Chang, JM., Kloks, T., Wang, HL. (2016). Gray Codes for AT-Free Orders via Antimatroids. In: Lipták, Z., Smyth, W. (eds) Combinatorial Algorithms. IWOCA 2015. Lecture Notes in Computer Science(), vol 9538. Springer, Cham. https://doi.org/10.1007/978-3-319-29516-9_7

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  • DOI: https://doi.org/10.1007/978-3-319-29516-9_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-29515-2

  • Online ISBN: 978-3-319-29516-9

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