The dynamic complexity of transitive closure is in DynTC0

William Hesse
2003 Theoretical Computer Science  
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 ÿrst-order update queries and aggregation operators, using a database with size polynomial in the size of the relation.
doi:10.1016/s0304-3975(02)00740-5 fatcat:jcdbk7gt5bejjk25v3dpefnm4a