Book ChapterDOI
Computing a Diameter-Constrained Minimum Spanning Tree in Parallel
Narsingh Deo,Ayman M. Abdalla +1 more
- pp 17-31
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A one-time-treeconstruction 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, and a parallel implementation of these heuristics on the MasPar MP-1 -- a massively parallel SIMD machine with 8192 processors.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 NPcomplete, for all values of k; 4 ≤ k ≤ (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-treeconstruction 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.read more
Citations
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Proceedings ArticleDOI
Greedy heuristics and an evolutionary algorithm for the bounded-diameter minimum spanning tree problem
TL;DR: A new randomized greedy heuristic builds a bounded-diameter spanning tree from its center vertex or vertices that chooses each next vertex at random but attaches the vertex with the lowest-weight eligible edge.
Journal ArticleDOI
Greedy heuristics for the bounded diameter minimum spanning tree problem
TL;DR: On Euclidean problem instances with small diameter bounds, the randomized heuristic is superior to the two fully greedy algorithms, though its advantage fades as the diameter bound grows.
Journal ArticleDOI
Improved heuristics for the bounded-diameter minimum spanning tree problem
Alok Singh,Ashok Kumar Gupta +1 more
TL;DR: This work has modified the crossover and mutation operators and the decoder used in permutation-coded evolutionary algorithm so as to improve its performance and obtained better quality solutions in a much shorter time.
Book ChapterDOI
Solving Diameter Constrained Minimum Spanning Tree Problems in Dense Graphs
TL;DR: First ever computational results are presented here for complete graph instances of the Diameter Constrained Minimum Spanning Tree Problem, andarse graph instances as large as those found in the literature were solved to proven optimality.
Book ChapterDOI
Encoding Bounded-Diameter Spanning Trees with Permutations and with Random Keys
TL;DR: A genetic algorithm that encodes spanning trees with random keys is as effective as one whose genotypes are permutations of vertices in comparisons on a variety of instances of the bounded-diameter minimum spanning tree problem.
References
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Book
Computers and Intractability: A Guide to the Theory of NP-Completeness
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
Journal ArticleDOI
A tree-based algorithm for distributed mutual exclusion
TL;DR: An algorithm for distributed mutual exclusion in a computer network of N nodes that communicate by messages rather than shared memory that does not require sequence numbers as it operates correctly despite message overtaking is presented.