Reachability is in DynFO
Logic in Computer Science
2017-04-06 v3 Computational Complexity
Data Structures and Algorithms
Abstract
Patnaik and Immerman introduced the dynamic complexity class DynFO of database queries that can be maintained by first-order dynamic programs with the help of auxiliary relations under insertions and deletions of edges (Patnaik and Immerman 1997). This article confirms their conjecture that the Reachability query is in DynFO. As a byproduct it is shown that the rank of a matrix with small values can be maintained in DynFO(+,x). It is further shown that the (size of the) maximum matching of a graph can be maintained in non-uniform DynFO, another extension of DynFO, with non-uniform initialisation of the auxiliary relations.
Keywords
Cite
@article{arxiv.1502.07467,
title = {Reachability is in DynFO},
author = {Samir Datta and Raghav Kulkarni and Anish Mukherjee and Thomas Schwentick and Thomas Zeume},
journal= {arXiv preprint arXiv:1502.07467},
year = {2017}
}