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MultiExchange Neighborhood Structures for the Capacitated Minimum Spanning Tree Problem
 MATHEMATICAL PROGRAMMING
, 2000
"... The capacitated minimum spanning tree (CMST) problem is to find a minimum cost spanning tree with an additional cardinality constraint on the sizes of the subtrees incident to a given root node. The CMST problem is an NPcomplete problem, and existing exact algorithms can solve only small size probl ..."
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Cited by 11 (3 self)
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The capacitated minimum spanning tree (CMST) problem is to find a minimum cost spanning tree with an additional cardinality constraint on the sizes of the subtrees incident to a given root node. The CMST problem is an NPcomplete problem, and existing exact algorithms can solve only small size problems. Currently, the best available heuristic procedures for the CMST problem are tabu search algorithms due to Amberg et al. and Sharaiha et al. These algorithms use twoexchange neighborhood structures that are based on exchanging a single node or a set of nodes between two subtrees. In this paper, we generalize their neighborhood structures to allow exchanges of nodes among multiple subtrees simultaneously; we refer to such neighborhood structures as multiexchange neighborhood structures. Our first multiexchange neighborhood structure allows exchanges of single nodes among several subtrees. Our second multiexchange neighborhood structure allows exchanges that involve multiple subtrees. The size of each of these neighborhood structures grows exponentially with the problem size without any substantial increase in the computational times needed to find improved neighbors. Our approach, which is based on the cyclic transfer neighborhood structure due to Thompson and Psaraftis and Thompson and Orlin transforms a profitable exchange into a negative cost subsetdisjoint cycle in a graph, called an improvement graph, and identifies these cycles using variants of shortest path labelcorrecting algorithms. Our computational results with GRASP and tabu search algorithms based on these neighborhood structures reveal that (i) for the unit demand case our algorithms obtained the best available solutions for all benchmark instances and improved some; and (ii) for the heterogeneous deman...
Solving General Ring Network Design Problems by MetaHeuristics
"... Ring network design problems have many important applications, especially in the field of telecommunications and vehicle routing. Those problems generally consist of constructing a ring network by selecting a node subset and corresponding direct links. Different requirements and objectives lead to ..."
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Cited by 7 (5 self)
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Ring network design problems have many important applications, especially in the field of telecommunications and vehicle routing. Those problems generally consist of constructing a ring network by selecting a node subset and corresponding direct links. Different requirements and objectives lead to various specific types of NPhard ring network design problems reported in the literature, each with its own algorithms. We exploit the similarities in problems to produce a more general problem formulation and associated solution methods that apply to a broad range of problems. Computational results are reported for an implementation using a metaheuristics framework with generic components for heuristic search.
Approximation Algorithms for the Capacitated Minimum Spanning Tree Problem and its Variants in Network Design
, 2004
"... Given an undirected graph G = (V, E) with nonnegative costs on its edges, a root node r V with demand v D wishing to route w(v) units of flow (weight) to r, and a positive number k, the Capacitated Minimum Steiner Tree (CMStT) problem asks for a minimum Steiner tree, rooted at r, spannin ..."
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Cited by 6 (4 self)
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Given an undirected graph G = (V, E) with nonnegative costs on its edges, a root node r V with demand v D wishing to route w(v) units of flow (weight) to r, and a positive number k, the Capacitated Minimum Steiner Tree (CMStT) problem asks for a minimum Steiner tree, rooted at r, spanning the vertices in D in which the sum of the vertex weights in every subtree hanging o# r is at most k. When D = V , this problem is known as the Capacitated Minimum Spanning Tree (CMST) problem. Both CMStT and CMST problems are NPhard. In this paper, we present approximation algorithms for these problems and several of their variants in network design. Our main results are the following.
Ring Network Design for Metropolitan Area Networks
, 1998
"... We consider the problem of designing ring networks for metropolitan area networks. Given a number of nodes representing locations that may be connected, the task is to construct a ring network by selecting a node subset and corresponding direct links. Any two nodes on the ring are enabled to communi ..."
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Cited by 5 (2 self)
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We consider the problem of designing ring networks for metropolitan area networks. Given a number of nodes representing locations that may be connected, the task is to construct a ring network by selecting a node subset and corresponding direct links. Any two nodes on the ring are enabled to communicate with each other so that the network provider gains a certain revenue. On the other hand, construction costs are incurred for the design of each direct link. The basic objective is to maximize the sum of all revenues minus the construction costs while building a ring network. We discuss certain relationships to other problems. Mathematical models are presented and used to obtain optimal solutions for small problem instances and upper bounds. We focus on the application of modern heuristic search concepts by means of a framework with generic components for heuristic search which enables the efficient adaptation to real world problems.
A Predecessor Coding in an Evolutionary Algorithm for the Capacitated Minimum Spanning Tree Problem
 Late Breaking Papers at the 2000 Genetic and Evolutionary Computation Conference, pages 309–316, Las Vegas, NV
"... This article presents an evolutionary algorithm (EA) for the capacitated minimum spanning tree problem occurring in telecommunication applications. The EA encodes a solution by a predecessor vector indicating for each node the preceding node at the path to the given central root node. Initiali ..."
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Cited by 5 (3 self)
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This article presents an evolutionary algorithm (EA) for the capacitated minimum spanning tree problem occurring in telecommunication applications. The EA encodes a solution by a predecessor vector indicating for each node the preceding node at the path to the given central root node. Initialization, crossover, and mutation operators were specifically designed to provide strong locality and to enable an e#ective search in the space of feasible solutions only. Furthermore, local heuristics are applied to promote the inclusion of lowcost links. Empirical results on a set of standard test problems indicate that the EA performs better than two other heuristic techniques.
Survivable Network Design: The Capacitated Minimum Spanning Network Problem
 In Proc. 7th INFORMS Telecommunications Conf
, 2004
"... We are given an undirected graph G = (V; E) with positive weights on its vertices representing demands, and nonnegative costs on its edges. Also given are a capacity constraint k, and root vertex r 2 V . In this paper, we consider the capacitated minimum spanning network (CMSN) problem, which as ..."
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Cited by 4 (2 self)
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We are given an undirected graph G = (V; E) with positive weights on its vertices representing demands, and nonnegative costs on its edges. Also given are a capacity constraint k, and root vertex r 2 V . In this paper, we consider the capacitated minimum spanning network (CMSN) problem, which asks for a minimum cost spanning network such that the the removal of r and its incident edges breaks the network into a number of components (groups), each of which is 2edgeconnected with a total weight of at most k. We show that the CMSN problem is NPhard, and present a 4approximation algorithm for graphs satisfying triangle inequality. We also show how to obtain similar approximation results for a related 2vertexconnected CMSN problem.
Load Balancing In HopByHop Routing With And Without Traffic Splitting
, 2003
"... This dissertation presents an exploration on solving traffic load balancing problems concentrating on the IP layer in hopbyhop networks. The first part of the traffic load balancing research is focused on bandwidthsensitive routing for premium class traffic in Differentiated Service (DiffServ) ..."
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Cited by 2 (0 self)
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This dissertation presents an exploration on solving traffic load balancing problems concentrating on the IP layer in hopbyhop networks. The first part of the traffic load balancing research is focused on bandwidthsensitive routing for premium class traffic in Differentiated Service (DiffServ) networks, where bandwidth usage of the premium class traffic is critical not only for the traffic itself, but also for other classes of traffic with lower priorities in the same network, such as the assured or best effort traffic. If the traffic in a network is splittable, then the second part of the load balancing research is intradomain traffic engineering in the network, where the bandwidthsensitive routing solutions in the first part can be used to achieve better traffic load balancing results in this part.
Dynamic Capacitated Minimum Spanning Trees
 In Proc. 3rd Intl. Conf. on Networking (ICN
, 2004
"... Given a set of terminals, each associated with a positive number denoting the traffic to be routed to a central terminal (root), the Capacitated Minimum Spanning Tree (CMST) problem asks for a minimum spanning tree, spanning all terminals, such that the amount of traffic routed from a subtree, linke ..."
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Cited by 2 (2 self)
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Given a set of terminals, each associated with a positive number denoting the traffic to be routed to a central terminal (root), the Capacitated Minimum Spanning Tree (CMST) problem asks for a minimum spanning tree, spanning all terminals, such that the amount of traffic routed from a subtree, linked to the root by an edge, does not exceed the given capacity constraint k. The CMST problem is NPcomplete and has been extensively studied for the past 40 years. Current best heuristics, in terms of cost and computation time (O(n log n)), are due to Esau and Williams [1], and Jothi and Raghavachari [2].
A hybrid ACO algorithm for the Capacitated Minimum Spanning Tree Problem
"... The problem of finding a Capacitated Minimum Spanning Tree asks for connecting a set of client nodes to a root node through a minimum cost tree network, subject to capacity constraints on all links. This paper reports on our design, implementation and performance evaluation of a hybrid Ant Colony Op ..."
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Cited by 2 (0 self)
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The problem of finding a Capacitated Minimum Spanning Tree asks for connecting a set of client nodes to a root node through a minimum cost tree network, subject to capacity constraints on all links. This paper reports on our design, implementation and performance evaluation of a hybrid Ant Colony Optimization algorithm for finding Capacitated Minimum Spanning Trees. Our Ant Colony Optimization algorithm is based on two important problem characteristics, namely the close relationship of the Capacitated Minimum Spanning Tree Problem with both the Capacitated Vehicle Routing Problem and the Minimum Spanning Tree Problem and hybridizes the Savings based Ant System with the algorithm of Prim, which is used to solve the subproblems of finding minimal spanning trees exactly. To assess the performance of our implementation we perform a computational study on a set of well known benchmark instances. For these instances our results show both the effectiveness and the efficiency of our algorithm when compared to several other stateoftheart techniques. 1
Memory Adaptive Reasoning & Greedy Assignment Techniques For The Capacitated Minimum Spanning Tree Problem
"... : It is the purpose of this paper to investigate e#ects of adding randomization to a memorybased heuristic. The algorithms we propose are applied to the Capacitated Minimum Spanning Tree problem (CMST), and we study the combined e#ects of simultaneously applying a memorybased and a randombased ..."
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Cited by 2 (0 self)
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: It is the purpose of this paper to investigate e#ects of adding randomization to a memorybased heuristic. The algorithms we propose are applied to the Capacitated Minimum Spanning Tree problem (CMST), and we study the combined e#ects of simultaneously applying a memorybased and a randombased heuristic to the CMST. This paper uses the Adaptive Reasoning Technique (ART) and concepts from the greedy randomized adaptive search procedure for solving the CMST. The resulting hybrid procedure is tested against the standalone EsauWilliams heuristic procedure, as well as the standalone greedy assignment technique. We find that randomization does not constructively add to the memorybased procedure, as ART alone typically outperforms all other approaches in terms of solution quality, while expending a modest amount of computational e#ort. 33.1 INTRODUCTION The capacitated minimum spanning tree problem (CMST) plays an important role in the design of backbone telecommunications ...