Algorithmica

, Volume 76, Issue 2, pp 445–473 | Cite as

Succinct Posets

Article

Abstract

We design a succinct data structure for representing a poset that, given two elements, can report whether one precedes the other in constant time. This is equivalent to succinctly representing the transitive closure graph of the poset, and we note that the same method can also be used to succinctly represent the transitive reduction graph. For an n element poset, the data structure occupies \(n^2/4 + o(n^2)\) bits in the worst case. Furthermore, a slight extension to this data structure yields a succinct oracle for reachability in arbitrary directed graphs. Thus, using no more than a quarter of the space required to represent an arbitrary directed graph, reachability queries can be supported in constant time. We also consider the operation of listing all the successors or predecessors of a given element, and show how to do this in constant time per element reported using a slightly modified version of our succinct data structure.

Keywords

Succinct data structure Graph representations Partial orders Rank and select Zarankiewicz problem Balanced bipartite graphs Graph compression Data compression 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.David R. Cherition School of Computer ScienceUniversity of WaterlooWaterlooCanada
  2. 2.Max Planck Institut für InformatikSaarbrückenGermany

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