CIAC 2015: Algorithms and Complexity pp 47-60 | Cite as

A Refined Complexity Analysis of Finding the Most Vital Edges for Undirected Shortest Paths

  • Cristina Bazgan
  • André  Nichterlein
  • Rolf Niedermeier
Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9079)

Abstract

We study the NP-hard Shortest Path Most Vital Edges problem arising in the context of analyzing network robustness. For an undirected graph with positive integer edge lengths and two designated vertices \(s\) and \(t\), the goal is to delete as few edges as possible in order to increase the length of the (new) shortest \(st\)-path as much as possible. This scenario has been mostly studied from the viewpoint of approximation algorithms and heuristics, while we particularly introduce a parameterized and multivariate point of view. We derive refined tractability as well as hardness results, and identify numerous directions for future research. Among other things, we show that increasing the shortest path length by at least one is much easier than to increase it by at least two.

Keywords

Short Path Minimum Span Tree Vertex Cover Cluster Graph Edge Deletion 
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 International Publishing Switzerland 2015

Authors and Affiliations

  • Cristina Bazgan
    • 1
    • 2
  • André  Nichterlein
    • 3
  • Rolf Niedermeier
    • 3
  1. 1.PSL, Université Paris-Dauphine, LAMSADE UMR CNRSParisFrance
  2. 2.Institut Universitaire de FranceParisFrance
  3. 3.Institut für Softwaretechnik und Theoretische InformatikTU BerlinGermany

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