Maintaining transitive closure in first order after node-set and edge-set deletions

doi:10.1016/S0020-0190(97)00066-5

Information Processing Letters

Volume 62, Issue 4, 28 May 1997, Pages 193-199

https://doi.org/10.1016/S0020-0190(97)00066-5 Get rights and content

Abstract

We consider the problem of maintaining, using first-order formulas but without auxiliary relations, the transitive closure of directed graphs after the deletion of sets of edges and nodes; earlier results focused on edge-set insertions and single edge deletions. We give a generic result which asserts maintainability after deleting any “antichain” of edges. Many maintainability results follow, including after deleting any edge from acyclic graphs, after deleting any subset of all incoming (outgoing) edges to (from) any antichain family of strongly connected components (SCC), and after deleting any antichain of nodes. We then show maintainability after deleting all edges (or nodes) in any antichain family of SCCs. Finally, we show that maintainability after node deletions is at least as hard as after edge deletions.

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^∗: This author gratefully acknowledges support of the Australian Research Council through research grants.

¹: Work by this author was supported by an OPRS and an MUPS scholarship.

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Maintaining transitive closure in first order after node-set and edge-set deletions

Abstract

Inform. and Comput.

Foundations of Databases

Maintenance of stratified databases viewed as a belief revision system

Foundations of Computer Science

Efficiently updating materialized views

On impossibility of decremental recomputation of recursive queries in relational calculus and SQL

First-order incremental evaluation of datalog queries

Increment boundedness and nonrecursive incremental evaluation of datalog queries

Space bounded FOIES