ESA 1993: Algorithms—ESA '93 pp 372-383 | Cite as

A fully dynamic data structure for reachability in planar digraphs

  • Sairam Subramanian
Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 726)

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.

Keywords

Planar Graph Directed Path Boundary Node Dynamic Algorithm Dummy Node 
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 1993

Authors and Affiliations

  • Sairam Subramanian
    • 1
  1. 1.Brown UniversityUSA

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