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Dynamically switching vertices in planar graphs

Extended abstract
  • Daniele Frigioni
  • Giuseppe F. Italiano
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1284)

Abstract

We consider graphs whose vertices may be in one of two different states: either on or off. We wish to maintain dynamically such graphs under an intermixed sequence of updates and queries. An update may reverse the status of a vertex, by switching it either on or off, and may insert a new edge or delete an existing edge. A query tests properties of the subgraph induced by the vertices that are on. We give efficient algorithms that maintain information about connectivity on planar graphs in O(log3n) amortized time per query, insert, delete, switch-on and switch-off operation over sequences of at least Ω(n) operations, where n is the number of vertices of the graph.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Daniele Frigioni
    • 1
  • Giuseppe F. Italiano
    • 2
  1. 1.Dipartimento di Informativa e SistemisticaUniversità di Roma “La Sapienza”RomaItaly
  2. 2.Dipartimento di Matematica Applicata ed InformativaUniversità “Ca' Foscari” di VeneziaVeniceItaly

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