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Finding the Most Vital Node of a Shortest Path

  • Enrico Nardelli
  • Guido Proietti
  • Peter Widmayer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2108)

Abstract

In an undirected, 2-node connected graph G = (V,E) with positive real edge lengths, the distance between any two nodes r and s is the length of a shortest path between r and s in G. The removal of a node and its incident edges from G mayincrease the distance from r to s. A most vital node of a given shortest path from r to s is a node (other than r and s) whose removal from G results in the largest increase of the distance from r to s. In the past, the problem of finding a most vital node of a given shortest path has been studied because of its implications in network management, where it is important to know in advance which component failure will affect network efficiency the most. In this paper, we show that this problem can be solved in O(m + n log n) time and O(m) space, where m and n denote the number of edges and the number of nodes in G.

Keywords

Short Path Incident Edge Node Failure Short Path Tree Short Path Tree 
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 2001

Authors and Affiliations

  • Enrico Nardelli
    • 1
    • 2
  • Guido Proietti
    • 1
    • 2
  • Peter Widmayer
    • 3
  1. 1.Dipartimento di Matematica Pura ed ApplicataUniversitá di L’AquilaL’AquilaItaly
  2. 2.Istituto di Analisi dei Sistemi ed InformaticaConsiglio Nazionale delle RicercheRomaItaly
  3. 3.Institut für Theoretische InformatikETH ZentrumZürichSwitzerland

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