Polynomial Time Algorithms for 2-Edge-Connectivity Augmentation Problems (Articolo in rivista)

Type
Label
  • Polynomial Time Algorithms for 2-Edge-Connectivity Augmentation Problems (Articolo in rivista) (literal)
Anno
  • 2003-01-01T00:00:00+01:00 (literal)
Alternative label
  • Galluccio, A.; Proietti, G. (2003)
    Polynomial Time Algorithms for 2-Edge-Connectivity Augmentation Problems
    in Algorithmica
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • Galluccio, A.; Proietti, G. (literal)
Pagina inizio
  • 361 (literal)
Pagina fine
  • 374 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
  • 36(4) (literal)
Rivista
Note
  • ISI Web of Science (WOS) (literal)
Titolo
  • Polynomial Time Algorithms for 2-Edge-Connectivity Augmentation Problems (literal)
Abstract
  • Given a 2-edge-connected, real weighted graph $G$ with $n$ vertices and $m$ edges, the 2-edge-connectivity augmentation problem is that of finding a minimum weight set of edges of $G$ to be added to a spanning subgraph $H$ of $G$ to make it 2-edge-connected. While the general problem is NP-hard and $-approximable, in this paper we prove that it becomes polynomial time solvable if $H$ is a depth-first search tree of $G$. More precisely, we provide an efficient algorithm for solving this special case which runs in ${\cal O}\big(M \cdot \alpha(M,n)\big)$ time, where $\alpha$ is the classic inverse of the Ackermann's function and $M=m \cdot \alpha(m,n)$. This algorithm has two main consequences: first, it provides a faster $-approximation algorithm for the general $-edge-connectivity augmentation problem; second, it solves in ${\cal O}(m \cdot \alpha(m,n))$ time the problem of restoring, by means of a minimum weight set of replacement edges, the $-edge-connectivity of a 2-edge-connected communication network undergoing a link failure. (literal)
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