Decremental maintenance of reachability in hypergraphs and minimum models of horn formulae

  • Giorgio Ausiello
  • Paolo Giulio Franciosa
  • Daniele Frigioni
  • Roberto Giaccio
Session 3B
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1350)


In this paper we present a decremental algorithm for maintaining minimum rank hyperpaths in a directed hypergraph from a source vertex s to all other vertices, under the assumption of unit hyperedge weights. Given a hypergraph H with n vertices and m hyperedges, the total time needed to perform a sequence of m hyperedge deletions is O(n · Size(H)), where Size(H) is the sum of the sizes of the hyperedges of H; the total space needed is O(n + Size(H)). In the case of integer hyperedge weights in [1, C] our solution requires O(C · n · Size(H)) total time and O(C + n + Size(H)) space.

Using the algorithm presented in this paper, we also show how to maintain the satisfiability and the minimum model of a Horn formula F with n propositional symbols in total time O(n·Length(F)) over any sequence of clause deletions.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Giorgio Ausiello
    • 1
  • Paolo Giulio Franciosa
    • 1
  • Daniele Frigioni
    • 1
  • Roberto Giaccio
    • 1
  1. 1.Dipartimento di Informatica e SistemisticaUniversità di Roma “La Sapienza”RomaItaly

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