Abstract:
This paper presents a fully dynamic algorithm for maintaining the transitive closure of a binary relation. All updates and queries can be computed by constant depth threshold circuits of polynomial size (TC 0 circuits). This places dynamic transitive closure in the dynamic complexity class DynTC 0, and implies that transitive closure can be maintained in database systems that include first-order update queries and aggregation operators, using a database with size polynomial in the size of the relation. 1
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