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A new 0–1 ILP approach for the bounded diameter minimum spanning tree problem
 Proceedings of the 2nd International Network Optimization Conference
, 2005
"... The bounded diameter minimum spanning tree (BDMST) problem is NPhard and appears e.g. in communication network design when considering certain quality of service requirements. Prior exact approaches for the BDMST problem mostly rely on network flowbased mixed integer linear programming and Miller ..."
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The bounded diameter minimum spanning tree (BDMST) problem is NPhard and appears e.g. in communication network design when considering certain quality of service requirements. Prior exact approaches for the BDMST problem mostly rely on network flowbased mixed integer linear programming and MillerTuckerZemlinbased formulations. This article presents a new, compact 0–1 integer linear programming model, which is further strengthened by dynamically adding violated connection and cycle elimination constraints within a branchandcut environment. The proposed approach is empirically compared to two recently published formulations. It turns out to work well in particular on dense instances with tight diameter bounds.
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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Cited by 10 (0 self)
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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...
The Economic Addition of Functionality to a Network
 In Proc. of High Performance Computing and Networking
, 1997
"... . In the operation of communication and computer networks, it may become desirable or necessary to add a new function to the network through the placement of the corresponding electronic device within certain existing user locations. This will involve deciding which user locations will have devices ..."
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. In the operation of communication and computer networks, it may become desirable or necessary to add a new function to the network through the placement of the corresponding electronic device within certain existing user locations. This will involve deciding which user locations will have devices placed at them as well as deciding an assignment of users to device locations. The objective when adding the new function is to choose these locations and assignments such that the combined cost of placing the devices and routing users to their assigned device locations is minimized. This problem, which we call the device placement problem, is closely related to the simple plant location problem and the pmedian problem. Like these problems, the device placement problem is NPhard, and thus it is highly unlikely that efficient methods for solving this problem to optimality exist. We discuss and test several heuristic methods for the device placement problem, as well as a very efficient meth...
A sharp threshold for minimum boundeddepth and boundeddiameter spanning trees and Steiner trees in random networks
, 2008
"... ..."
A New Approach to the Simple Plant Location Problem
"... In this paper we show the relation between the simple plant location problem (SPLP), a location facility analysis problem where no capacities are set a priori, and the device placement problem, a problem issued from the telecommunication field. We give the reductions from one problem to the other, p ..."
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In this paper we show the relation between the simple plant location problem (SPLP), a location facility analysis problem where no capacities are set a priori, and the device placement problem, a problem issued from the telecommunication field. We give the reductions from one problem to the other, presenting also one of the tools to deal with the device placement problem given in [5], and an approximate optimization method based on that idea for the SPLP. 1. INTRODUCTION "Facility location analysis deals with the problem of location one of several facilities with regard to existing facilities and client in order to optimize some economic criterion. Examples of facilities are plants, warehouses, schools, hospitals, administrative buildings, department stores, waste, material dumps, ambulance of fire engine depots, etc." [15] In this paper we show the relation between the simple plant location problem (SPLP), a location facility analysis problem where no capacities are set a priori, and...
An Ant Colony . . . for the Bounded Diameter Minimum Spanning Tree Problem
, 2006
"... ... das durchmesserbeschränkte minimale Spannbaum Problem erarbeitet. Bei diesem Problem handelt es sich um ein N Pschweres kombinatorisches Optimierungsproblem mit zahlreichen praktischen Anwendungsgebieten, zum Beispiel im Netzwerkdesign. Der Algorithmus wurde mit einer lokalen Optimierungsheu ..."
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... das durchmesserbeschränkte minimale Spannbaum Problem erarbeitet. Bei diesem Problem handelt es sich um ein N Pschweres kombinatorisches Optimierungsproblem mit zahlreichen praktischen Anwendungsgebieten, zum Beispiel im Netzwerkdesign. Der Algorithmus wurde mit einer lokalen Optimierungsheuristik, nämlich einem Variable Neighbourhood Descent, erweitert. Diese lokale Optimierungsheuristik arbeitet auf vier verschiedenen Nachbarschaftsstrukturen, bei deren Entwicklung besonders auf eine effiziente Evaluierung der Nachbarschaft einer Lösung Wert gelegt wurde. Vergleiche mit verschiedenen evolu