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Compact Representation of Posets

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Algorithms and Computation (ISAAC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7074))

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Abstract

We give a data structure for storing an n-element poset of width w in essentially minimal space. We then show how this data structure supports the most interesting queries on posets in either constant time, or in time that depends only on w and the size of the in-/output, but not on n. Our results also have direct applicability to DAGs of low width.

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References

  1. Aho, A.V., Garey, M.R., Ullman, J.D.: The transitive reduction of a directed graph. SIAM J. Comput. 1(2), 131–137 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  2. Brightwell, G., Goodall, S.: The number of partial orders of fixed width. Order 13(4), 315–337 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  3. Daskalakis, C., Karp, R.M., Mossel, E., Riesenfeld, S., Verbin, E.: Sorting and selection in posets. SIAM J. Comput. 40(3), 597–622 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  4. Dhar, D.: Entropy and phase transitions in partially ordered sets. J. Math. Phys. 19(8), 1711–1713 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  5. Farzan, A., Munro, J.I.J.: Succinct Representation of Arbitrary Graphs. In: Halperin, D., Mehlhorn, K. (eds.) Esa 2008. LNCS, vol. 5193, pp. 393–404. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  6. Moyles, D.M., Thompson, G.L.: An algorithm for finding a minimum equivalent graph of a digraph. J. ACM 16(3), 455–460 (1969)

    Article  MATH  Google Scholar 

  7. Munro, J.I., Raman, R., Raman, V., Rao, S.S.: Succinct Representations of Permutations. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 345–356. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  8. Munro, J.I., Raman, V.: Succinct representation of balanced parentheses and static trees. SIAM J. Comput. 31(3), 762–776 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  9. Talamo, M., Vocca, P.: An efficient data structure for lattice operations. SIAM J. Comput. 28(5), 1783–1805 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  10. Thorup, M.: Compact oracles for reachability and approximate distances in planar digraphs. J. ACM 51(6), 993–1024 (2004)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Max-Planck-Institut für Informatik, Saarbrücken, Germany

    Arash Farzan

  2. Karlsruhe Institute of Technology, Karlsruhe, Germany

    Johannes Fischer

Authors
  1. Arash Farzan
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  2. Johannes Fischer
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Editor information

Editors and Affiliations

  1. Chuo University, Kasuga, Bunkyo-ku, 112-8551, Tokyo, Japan

    Takao Asano

  2. Gunma University, 1-5-1 Tenjin-Cho, 376-8515, Kiryu-Shi, Japan

    Shin-ichi Nakano

  3. Japan Advanced Institute of Science and Technology, 1-1 Asahidai, 923-1292, Nomi, Ishikawa, Japan

    Yoshio Okamoto

  4. Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, 152-8552, Tokyo, Japan

    Osamu Watanabe

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© 2011 Springer-Verlag Berlin Heidelberg

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Farzan, A., Fischer, J. (2011). Compact Representation of Posets. In: Asano, T., Nakano, Si., Okamoto, Y., Watanabe, O. (eds) Algorithms and Computation. ISAAC 2011. Lecture Notes in Computer Science, vol 7074. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25591-5_32

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  • DOI: https://doi.org/10.1007/978-3-642-25591-5_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25590-8

  • Online ISBN: 978-3-642-25591-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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