Graphical evolution: an introduction to the theory of random graphs
Graphical evolution: an introduction to the theory of random graphs
A tree-based algorithm for distributed mutual exclusion
ACM Transactions on Computer Systems (TOCS)
A note on Raymond's tree based algorithm for distributed mutual exclusion
Information Processing Letters
Distributed Operating Systems and Algorithms
Distributed Operating Systems and Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A Tree-Based Distributed Algorithm for the K-Entry Critical Section Problem
Proceedings of the 1994 International Conference on Parallel and Distributed Systems
Greedy heuristics for the bounded diameter minimum spanning tree problem
Journal of Experimental Algorithmics (JEA)
Diameter-constrained steiner tree
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
Improvement of bounded-diameter MST instances with hybridization of multi-objective EA
Proceedings of the 2011 International Conference on Communication, Computing & Security
Multiobjective network topology design
Applied Soft Computing
Multiobjective EA approach for improved quality of solutions for spanning tree problem
EMO'05 Proceedings of the Third international conference on Evolutionary Multi-Criterion Optimization
HiPC'04 Proceedings of the 11th international conference on High Performance Computing
Minimum diameter cost-constrained Steiner trees
Journal of Combinatorial Optimization
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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.