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Computational methods for the diameter restricted minimum weight spanning tree problem
 Australasian Journal of Combinatorics
, 1994
"... Let G be a simple undirected graph with nonnegative edge weights. In this paper we consider the following combinatorial optimization problem: Find, in G, a minimum weight spanning tree having diameter at most D. This problem is trivial for D:S 3 and NPcomplete for D:: 4. In this paper we develop a ..."
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Let G be a simple undirected graph with nonnegative edge weights. In this paper we consider the following combinatorial optimization problem: Find, in G, a minimum weight spanning tree having diameter at most D. This problem is trivial for D:S 3 and NPcomplete for D:: 4. In this paper we develop and implement a number of Branch and Bound algorithms for this problem. Computational results, based on simulated problems, are discussed. 1.
Computing A DiameterConstrained Minimum Spanning Tree
, 2001
"... In numerous practical applications, it is necessary to find the smallest possible tree with a bounded diameter. A diameterconstrained minimum spanning tree (DCMST) of a given undirected, edgeweighted graph, G, is the smallestweight spanning tree of all spanning trees of G which contain no path wi ..."
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In numerous practical applications, it is necessary to find the smallest possible tree with a bounded diameter. A diameterconstrained minimum spanning tree (DCMST) of a given undirected, edgeweighted graph, G, is the smallestweight spanning tree of all spanning trees of G which contain no path with more than k edges, where k is a given positive integer. The problem of finding a DCMST is NPcomplete for all values of k; 4 k (n  2), except when all edgeweights are identical. A DCMST is essential for the efficiency of various distributed mutual exclusion algorithms, where it can minimize the number of messages communicated among processors per critical section. It is also useful in linear lightwave networks, where it can minimize interference in the network by limiting the traffic in the network lines. Another practical application requiring a DCMST arises in data compression, where some algorithms compress a file utilizing a tree datastructure, and decompress a path in the tree to access a record. A DCMST helps such algorithms to be fast without sacrificing a lot of storage space. We present a survey of the literature on the DCMST problem, study the expected diameter of a random labeled tree, and present five new polynomialtime algorithms for an approximate DCMST. One of our new algorithms constructs an approximate DCMST in a modified greedy fashion, employing a heuristic for selecting an edge to be added to iii the tree in each stage of the construction. Three other new algorithms start with an unconstrained minimum spanning tree, and iteratively refine it into an approximate DCMST. We also present an algorithm designed for the special case when the diameter is required to be no more than 4. Such a diameter4 tree is also used for evaluating the quality of o...
Two New Algorithms for UMTS Access Network Topology Design
 EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
, 2005
"... Present work introduces two network design algorithms for planning UMTS (Universal Mobile Telecommunication System) access networks. The Task is ..."
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Present work introduces two network design algorithms for planning UMTS (Universal Mobile Telecommunication System) access networks. The Task is
Constraint Programming for the Diameter Constrained Minimum Spanning Tree Problem
"... Given an undirected connected graph G = (V,E) with a set V of vertices, a set E of edges, and costs cij associated to every edge [i,j] ∈ E, with i < j, the Diameter Minimum Spanning Tree Problem (DCMST) consists in finding a minimum spanning tree T = (V,E ′), with E ′ ⊆ E, where the diameter ..."
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Given an undirected connected graph G = (V,E) with a set V of vertices, a set E of edges, and costs cij associated to every edge [i,j] ∈ E, with i < j, the Diameter Minimum Spanning Tree Problem (DCMST) consists in finding a minimum spanning tree T = (V,E ′), with E ′ ⊆ E, where the diameter