The Minimum vulnerability problem

Assadi, S ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1007/s00453-014-9927-z
  3. Abstract:
  4. We revisit the problem of finding (Formula presented.) paths with a minimum number of shared edges between two vertices of a graph. An edge is called shared if it is used in more than one of the (Formula presented.) paths. We provide a (Formula presented.)-approximation algorithm for this problem, improving the best previous approximation factor of (Formula presented.). We also provide the first approximation algorithm for the problem with a sublinear approximation factor of (Formula presented.), where (Formula presented.) is the number of vertices in the input graph. For sparse graphs, such as bounded-degree and planar graphs, we show that the approximation factor of our algorithm can be improved to (Formula presented.). While the problem is NP-hard, and even hard to approximate to within an (Formula presented.) factor, we show that the problem is polynomially solvable when (Formula presented.) is a constant. This settles an open problem posed by Omran et al. regarding the complexity of the problem for small values of (Formula presented.). We present most of our results in a more general form where each edge of the graph has a sharing cost and a sharing capacity, and there is a vulnerability parameter (Formula presented.) that determines the number of times an edge can be used among different paths before it is counted as a shared/vulnerable edge
  5. Keywords:
  6. Approximation algorithms ; Inapproximability ; Network design ; Shared edges
  7. Source: Algorithmica ; Volume 70, Issue 4 , 2014 , pp 718-731 ; ISSN: 14320541
  8. URL: http://link.springer.com./article/10.1007%2Fs00453-014-9927-z