Single-Source Fully Dynamic Reachability

Keywords and Synonyms

Single-source fully dynamic transitive closure      

Problem Definition

A dynamic graph algorithm maintains a given property $\cal{P}$ on a graph subject to dynamic changes, such as edge insertions, edge deletions and edge weight updates. A dynamic graph algorithm should process queries on property $\cal{P}$ quickly, and perform update operations faster than recomputing from scratch, as carried out by the fastest static algorithm. An algorithm is fully dynamic if it can handle both edge insertions and edge deletions and partially dynamic if it can handle either edge insertions or edge deletions, but not both.

Given a graph with n vertices and m edges, the transitive closure (or reachability) problem consists of building an $n \times n$ Boolean matrix M such that $M[x,y]=1$ if and only if there is a directed path from vertex x to vertex y in the graph. The fully dynamic version of this problem can be defifined as follows:

Definition 1

(Fully dynamic...