Compact Representation of Posets

  • Arash Farzan
  • Johannes Fischer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7074)

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.

Keywords

Directed Acyclic Graph Transitive Closure Compact Representation Arbitrary Graph Transitive Reduction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 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)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Brightwell, G., Goodall, S.: The number of partial orders of fixed width. Order 13(4), 315–337 (1996)MathSciNetCrossRefMATHGoogle Scholar
  3. 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)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Dhar, D.: Entropy and phase transitions in partially ordered sets. J. Math. Phys. 19(8), 1711–1713 (1978)MathSciNetCrossRefMATHGoogle Scholar
  5. 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)CrossRefGoogle Scholar
  6. 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)CrossRefMATHGoogle Scholar
  7. 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)CrossRefGoogle Scholar
  8. 8.
    Munro, J.I., Raman, V.: Succinct representation of balanced parentheses and static trees. SIAM J. Comput. 31(3), 762–776 (2001)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Talamo, M., Vocca, P.: An efficient data structure for lattice operations. SIAM J. Comput. 28(5), 1783–1805 (1999)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Thorup, M.: Compact oracles for reachability and approximate distances in planar digraphs. J. ACM 51(6), 993–1024 (2004)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Arash Farzan
    • 1
  • Johannes Fischer
    • 2
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany
  2. 2.Karlsruhe Institute of TechnologyKarlsruheGermany

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