A fully dynamic data structure for reachability in planar digraphs

Abstract

In this paper we investigate the problem of maintaining all-pairs reachability information in a planar digraph G as it undergoes changes. We give a fully dynamic O(n)-space data structure to support an arbitrary sequence of operations that consist of adding new edges (or nodes), deleting some existing edge, and querying to find out if a given node v is reachable in G by a directed path from another node u. We show that using our data structure a reachability query between two nodes u and v can be performed in O(n2/3 log n) time, where n is the number of nodes in G. Additions and deletions of edges and nodes can also be handled within the same time bounds. The time for deletion is worst-case while the time for edge-addition is amortized. This is the first fully dynamic algorithm for the planar reachability problem that uses only sublinear time for both queries and updates.