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.
CITATION STYLE
Ausiello, G., Franciosa, P. G., Frigioni, D., & Giaccio, R. (1997). Decremental maintenance of reachability in hypergraphs and minimum models of horn formulae. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1350, pp. 122–131). Springer Verlag. https://doi.org/10.1007/3-540-63890-3_14
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