Maintaining the classes of 4-edge-connectivity in a graph on-line

Ye Dinitz, J. Westbrook

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

Two vertices of an undirected graph are called k-edge-connected if there exist k edge-disjoint paths between them (equivalently, they cannot be disconnected by the removal of less than k edges from the graph). Equivalence classes of this relation are called classes of k-edge-connectivity or k-edge-connected components. This paper describes graph structures relevant to classes of 4-edge-connectivity and traces their transformations as new edges are inserted into the graph. Data structures and an algorithm to maintain these classes incrementally are given. Starting with the empty graph, any sequence of q Same-4-Class? queries and n Insert-Vertex and m Insert-Edge updates can be performed in O(q+m+n log n) total time. Each individual query requires O(1) time in the worst-case. In addition, an algorithm for maintaining the classes of k-edge-connectivity (k arbitrary) in a (k - 1)-edge-connected graph is presented. Its complexity is O(q+m+n), with O(M+k2n log(n/k)) preprocessing, where M is the number of edges initially in the graph and n is the number of its vertices.

Original languageEnglish
Pages (from-to)242-276
Number of pages35
JournalAlgorithmica
Volume20
Issue number3
DOIs
StatePublished - 1 Jan 1998
Externally publishedYes

Keywords

  • Analysis of algorithms
  • Component
  • Connectivity class
  • Dynamic algorithm
  • Dynamic data structure
  • Edge-connectivity
  • Graph algorithm

Fingerprint

Dive into the research topics of 'Maintaining the classes of 4-edge-connectivity in a graph on-line'. Together they form a unique fingerprint.

Cite this