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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)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Brightwell, G., Goodall, S.: The number of partial orders of fixed width. Order 13(4), 315–337 (1996)MathSciNetCrossRefzbMATHGoogle 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)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Dhar, D.: Entropy and phase transitions in partially ordered sets. J. Math. Phys. 19(8), 1711–1713 (1978)MathSciNetCrossRefzbMATHGoogle 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)CrossRefzbMATHGoogle 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)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Talamo, M., Vocca, P.: An efficient data structure for lattice operations. SIAM J. Comput. 28(5), 1783–1805 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Thorup, M.: Compact oracles for reachability and approximate distances in planar digraphs. J. ACM 51(6), 993–1024 (2004)MathSciNetCrossRefzbMATHGoogle 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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