Parallel algorithms for the degree-constrained minimum spanning tree problem using nearest-neighbor chains and the heap-traversal technique

The degree-constrained minimum spanning tree (d-MST) problem attempts to find a minimum spanning tree with an added constraint that no nodes in the tree have a degree larger than a specified integer d. It is known that computing the d-MST is NP-hard for every d in the range 2 /spl les/ d /spl les/ (...

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Published in:Proceedings. International Conference on Parallel Processing Workshop pp. 398 - 404
Main Authors: Li-Jen Mao, Sheau-Dong Lang
Format: Conference Proceeding
Language:English
Published: IEEE 2002
Subjects:
Computer science
Heuristic algorithms
Information management
Iterative algorithms
Lagrangian functions
Nearest neighbor searches
Neural networks
Parallel algorithms
Traveling salesman problems
Tree graphs
ISBN:9780769516806, 0769516807
ISSN:1530-2016
Online Access:Get full text
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Abstract The degree-constrained minimum spanning tree (d-MST) problem attempts to find a minimum spanning tree with an added constraint that no nodes in the tree have a degree larger than a specified integer d. It is known that computing the d-MST is NP-hard for every d in the range 2 /spl les/ d /spl les/ (n - 2), where n denotes the total number of nodes. Several approximate algorithms (heuristics) have been proposed in the literature. We have previously proposed three approximate algorithms, IR, TC-RNN, and TC-NNC, for solving the d-MST problem, the last two (TC-RNN and TC-NNC) take advantage of nearest neighbors and their properties. Our experimental results showed that both the TC-RNN and TC-NNC algorithms consistently produce spanning trees with a smaller weight (better quality-of-solution) than that of IR, but using slightly longer execution time. We propose a new heap traversal technique that further improves the time efficiency of TC-RNN and TC-NNC. Our experiments using randomly generated, weighted graphs as inputs show that the TC-NNC algorithm outperforms the other two approximate algorithms in terms of the execution time and quality-of-solution.
AbstractList The degree-constrained minimum spanning tree (d-MST) problem attempts to find a minimum spanning tree with an added constraint that no nodes in the tree have a degree larger than a specified integer d. It is known that computing the d-MST is NP-hard for every d in the range 2 /spl les/ d /spl les/ (n - 2), where n denotes the total number of nodes. Several approximate algorithms (heuristics) have been proposed in the literature. We have previously proposed three approximate algorithms, IR, TC-RNN, and TC-NNC, for solving the d-MST problem, the last two (TC-RNN and TC-NNC) take advantage of nearest neighbors and their properties. Our experimental results showed that both the TC-RNN and TC-NNC algorithms consistently produce spanning trees with a smaller weight (better quality-of-solution) than that of IR, but using slightly longer execution time. We propose a new heap traversal technique that further improves the time efficiency of TC-RNN and TC-NNC. Our experiments using randomly generated, weighted graphs as inputs show that the TC-NNC algorithm outperforms the other two approximate algorithms in terms of the execution time and quality-of-solution.
Author Sheau-Dong Lang
Li-Jen Mao
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Snippet The degree-constrained minimum spanning tree (d-MST) problem attempts to find a minimum spanning tree with an added constraint that no nodes in the tree have a...
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StartPage 398
SubjectTerms Computer science
Heuristic algorithms
Information management
Iterative algorithms
Lagrangian functions
Nearest neighbor searches
Neural networks
Parallel algorithms
Traveling salesman problems
Tree graphs
Title Parallel algorithms for the degree-constrained minimum spanning tree problem using nearest-neighbor chains and the heap-traversal technique
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