Finding the k most vital edges with respect to minimum spanning tree

Research output: Contribution to conferencePaperpeer-review

20 Citations (Scopus)

Abstract

For a connected, undirected and weighted graph G = (V, E), the problem of finding the k most vital edges of G with respect to minimum spanning tree is to find k edges in G whose removal will cause greatest weight increase in the minimum spanning tree of the remaining graph. This problem is known to be NP-hard for arbitrary k. In this paper, we first describe a simple exact algorithm for this problem, based on the approach of edge replacement in the minimum spanning tree of G. Next we present polynomial-time randomized algorithms that produce optimal and approximate solutions to this problem. For |V| = n and |E| = m, our algorithm producing optimal solution has a time complexity of O(mn) with probability of success at least e -k 2/2(m-n-1)-2 log c k/k-4, c = 1+1/2 k/2, and the algorithm producing approximate solution runs in time O(mn+nk 2 log k) and yields results within factor 2 to the optimal one. Finally we show that both of our randomized algorithms can be easily parallelized. On a CREW PRAM, the first algorithm runs in O(n) time using n 2 processors, and the second algorithm runs in O(log 2 n) time using mn/log n processors.

Original languageEnglish
Pages255-262
Number of pages8
Publication statusPublished - 1997
Externally publishedYes
EventProceedings of the 1997 IEEE National Aerospace and Electronics Conference, NAECON. Part 1 (of 2) - Dayton, OH, USA
Duration: 14 Jul 199717 Jul 1997

Conference

ConferenceProceedings of the 1997 IEEE National Aerospace and Electronics Conference, NAECON. Part 1 (of 2)
CityDayton, OH, USA
Period14/07/9717/07/97

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