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Optimal Offline Dynamic 2, 3-Edge/Vertex Connectivity

  • Richard Peng
  • Bryce SandlundEmail author
  • Daniel D. Sleator
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11646)

Abstract

We give offline algorithms for processing a sequence of 2- and 3-edge and vertex connectivity queries in a fully-dynamic undirected graph. While the current best fully-dynamic online data structures for 3-edge and 3-vertex connectivity require \(O(n^{2/3})\) and O(n) time per update, respectively, our per-operation cost is only \(O(\log n)\), optimal due to the dynamic connectivity lower bound of Patrascu and Demaine. Our approach utilizes a divide and conquer scheme that transforms a graph into smaller equivalents that preserve connectivity information. This construction of equivalents is closely-related to the development of vertex sparsifiers, and shares important connections to several upcoming results in dynamic graph data structures, including online models.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Richard Peng
    • 1
  • Bryce Sandlund
    • 2
    Email author
  • Daniel D. Sleator
    • 3
  1. 1.School of Computer ScienceGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada
  3. 3.Department of Computer ScienceCarnegie Mellon UniversityPittsburghUSA

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