The Dynamic Complexity of Transitive Closure Is in DynTC°
This paper presents a fully dynamic algorithm for maintaining the transitive closure of a directed graph. All updates and queries can be computed by constant depth threshold circuits of polynomial size (TC° circuits). This places transitive closure in the dynamic complexity class DynTC°, and implies that transitive closure can be maintained in databases using updates written in a first order query language plus counting operators, while keeping the size of the database polynomial in the size of the graph.
KeywordsComplexity Class Transitive Closure Auxiliary Data Dynamic Algorithm Graph Reachability
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