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  • NC Algorithms for the single most vital edge problem with respect to all pairs shortest paths

    Author(s)
    Venema, Sven
    Shen, Hong
    Suraweera, Francis
    Griffith University Author(s)
    Suraweera, Francis
    Shen, Hong
    Venema, Sven
    Year published
    2000
    Metadata
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    Abstract
    For a weighted, undirected graph G=(V, E) where |V|=n and |E|=m, we examine the single most vital edge with respect to all-pairs shortest paths (APSP) under two different measurements. The first measurement considers only the impact of the removal of a single edge from the APSP on the shortest distance between each vertex pair. The second considers the total weight of all the edges which make up the APSP, that is, calculate the sum of the distance between each vertex pair after the deletion of any edge belonging to a shortest path. We give a sequential algorithm for this problem, and show how to obtain an NC algorithm running ...
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    For a weighted, undirected graph G=(V, E) where |V|=n and |E|=m, we examine the single most vital edge with respect to all-pairs shortest paths (APSP) under two different measurements. The first measurement considers only the impact of the removal of a single edge from the APSP on the shortest distance between each vertex pair. The second considers the total weight of all the edges which make up the APSP, that is, calculate the sum of the distance between each vertex pair after the deletion of any edge belonging to a shortest path. We give a sequential algorithm for this problem, and show how to obtain an NC algorithm running in O(log n) time using mn2 processors and O(mn2) space on the MINIMUM CRCW PRAM. Given the shortest distance between each pair of vertices u and v, the diameter of the graph is defined as the longest of these distances. The Most vital edge with respect to the diameter is the edge lying on such a u-v shortest path which when removed causes the greatest increase in the diameter. We show how to modify the above algorithm to solve this problem using the same time and number of processors. Both algorithms compare favourably with the straightforward solution which simply recalculates the all pairs shortest path information.
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    Journal Title
    Parallel Processing Letters
    Volume
    10
    Issue
    1
    Publisher URI
    http://www.worldscinet.com/ppl/10/1001/S012962640000007X.html
    Copyright Statement
    © 2000 World Scientific Publishing Company. The electronic version of the article is published as above.
    Subject
    History and Archaeology
    Distributed Computing
    Publication URI
    http://hdl.handle.net/10072/3229
    Collection
    • Journal articles

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