Computing a diameter-constrained minimum spanning tree in parallel

    Authors

    N. Deo;A. Abdalla

    Comments

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    Keywords

    DISTRIBUTED MUTUAL EXCLUSION; ALGORITHM; Computer Science, Theory & Methods

    Abstract

    A minimum spanning tree (MST) with a small diameter is required in numerous practical situations. It is needed, for example, in distributed mutual exclusion algorithms in order to minimize the number of messages communicated among processors per critical section. The Diameter-Constrained MST (DCMST) problem can be stated as follows: given an undirected, edge-weighted graph G with n nodes and a positive integer k, find a spanning tree with the smallest weight among all spanning trees of G which contain no path with more than k edges. This problem is known to be NP-complete, for all values of k; 4 less than or equal to k less than or equal to (n - 2). Therefore, one has to depend on heuristics and live with approximate solutions. In this paper, we explore two heuristics for the DCMST problem: First, we present a one-time-tree-construction algorithm that constructs a DCMST in a modified greedy fashion, employing a heuristic for selecting edges to be added to the tree at each stage of the tree construction. This algorithm is fast and easily parallelizable. It is particularly suited when the specified values for k are small-independent of n. The second algorithm starts with an unconstrained MST and iteratively refines it by replacing edges, one by one, in long paths until there is no path left with more than k edges. This heuristic was found to be better suited for larger values of k. We discuss convergence, relative merits, and parallel implementation of these heuristics on the MasPar MP-1- a massively parallel SIMD machine with 8192 processors. Our extensive empirical study shows that the two heuristics produce good solutions for a wide variety of inputs.

    Journal Title

    Algorithms and Complexity

    Volume

    1767

    Publication Date

    1-1-2000

    Document Type

    Article

    Language

    English

    First Page

    17

    Last Page

    31

    WOS Identifier

    WOS:000165334400002

    ISSN

    0302-9743; 3-540-67159-5

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