The Dynamic Complexity of Transitive Closure Is in DynTC°

  • William Hesse
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1973)


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.


Complexity Class Transitive Closure Auxiliary Data Dynamic Algorithm Graph Reachability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • William Hesse
    • 1
  1. 1.Department of Computer ScienceUniversity of MassachusettsAmherst

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