Abstract
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.
Work partially supported by European Union ESPRIT Long Term Research Project ALCOM-IT under contract no. 20244, and by Progetto Finalizzato Trasporti 2 of the Italian National Research Council.
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Ausiello, G., Franciosa, P.G., Frigioni, D., Giaccio, R. (1997). Decremental maintenance of reachability in hypergraphs and minimum models of horn formulae. In: Leong, H.W., Imai, H., Jain, S. (eds) Algorithms and Computation. ISAAC 1997. Lecture Notes in Computer Science, vol 1350. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63890-3_14
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DOI: https://doi.org/10.1007/3-540-63890-3_14
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