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Showing papers in "Networks in 2004"


Journal ArticleDOI
01 Oct 2004-Networks
TL;DR: In this paper, a solution procedure for the Elementary Shortest Path Problem with Resource Constraints (ESPPRC) is proposed, which extends the classical label correcting algorithm originally developed for the relaxed (nonelementary) path version of this problem.
Abstract: In this article, we propose a solution procedure for the Elementary Shortest Path Problem with Resource Constraints (ESPPRC). A relaxed version of this problem in which the path does not have to be elementary has been the backbone of a number of solution procedures based on column generation for several important problems, such as vehicle routing and crew pairing. In many cases relaxing the restriction of an elementary path resulted in optimal solutions in a reasonable computation time. However, for a number of other problems, the elementary path restriction has too much impact on the solution to be relaxed or might even be necessary. We propose an exact solution procedure for the ESPPRC, which extends the classical label correcting algorithm originally developed for the relaxed (nonelementary) path version of this problem. We present computational experiments of this algorithm for our specific problem and embedded in a column generation scheme for the classical Vehicle Routing Problem with Time Windows. © 2004 Wiley Periodicals, Inc. NETWORKS, Vol. 44(3), 216–229 2004

606 citations


Journal ArticleDOI
01 May 2004-Networks
TL;DR: This article formulates the Ring Star Problem as a mixed-integer linear program and strengthens it with the introduction of several families of valid inequalities that are shown to be facet-defining and are used to develop a branch-and-cut algorithm.
Abstract: In the Ring Star Problem, the aim is to locate a simple cycle through a subset of vertices of a graph with the objective of minimizing the sum of two costs: a ring cost proportional to the length of the cycle and an assignment cost from the vertices not in the cycle to their closest vertex on the cycle. The problem has several applications in telecommunications network design and in rapid transit systems planning. It is an extension of the classical location–allocation problem introduced in the early 1960s, and closely related versions have been recently studied by several authors. This article formulates the problem as a mixed-integer linear program and strengthens it with the introduction of several families of valid inequalities. These inequalities are shown to be facet-defining and are used to develop a branch-and-cut algorithm. Computational results show that instances involving up to 300 vertices can be solved optimally using the proposed methodology. © 2004 Wiley Periodicals, Inc.

169 citations


Journal ArticleDOI
01 Jul 2004-Networks
TL;DR: It is shown that the modulation of intensity matrices arising in cancer radiation therapy using multileaf collimators (MLC) is equivalent to decomposing a given integer matrix into a positive linear combination of (0, 1) matrices, and deduce that the column generation subproblem can be solved as a shortest path problem.
Abstract: In this article the modulation of intensity matrices arising in cancer radiation therapy using multileaf collimators (MLC) is investigated. It is shown that the problem is equivalent to decomposing a given integer matrix into a positive linear combination of (0, 1) matrices. These matrices, called shape matrices, must have the strict consecutive-1-property, together with another property derived from the technological restrictions of the MLC equipment. Various decompositions can be evaluated by their beam-on time (time during which radiation is applied to the patient) or the treatment time (beam-on time plus time for setups). We focus on the former, and develop a nonlinear mixed-integer programming formulation of the problem. This formulation can be decomposed to yield a column generation formulation: a linear program with a large number of variables that can be priced by solving a subproblem. We then develop a network model in which paths in the network correspond to feasible shape matrices. As a consequence, we deduce that the column generation subproblem can be solved as a shortest path problem. Furthermore, we are able to develop two alternative models of the problem as side-constrained network flow formulations, and so obtain our main theoretical result that the problem is solvable in polynomial time. Finally, a numerical comparison of our exact solutions with those of well-known heuristic methods shows that the beam-on time can be reduced by a considerable margin. © 2004 Wiley Periodicals, Inc.

114 citations


Journal ArticleDOI
01 May 2004-Networks
TL;DR: A greedy algorithm is formulated for MCDFP and a full characterization via forbidden subgraphs of the class of graphs is provided, for which this greedy algorithm always yields an optimum solution (for arbitrary choices of problem parameters).
Abstract: A dynamic network consists of a directed graph with capacities, costs, and integral transit times on the arcs. In the minimum-cost dynamic flow problem (MCDFP), the goal is to compute, for a given dynamic network with source s, sink t, and two integers v and T, a feasible dynamic flow from s to t of value v, obeying the time bound T, and having minimum total cost. MCDFP contains as subproblems the minimum-cost maximum dynamic flow problem, where v is fixed to the maximum amount of flow that can be sent from s to t within time T and the minimum-cost quickest flow problem, where is T is fixed to the minimum time needed for sending v units of flow from s to t. We first prove that both subproblems are NP-hard even on two-terminal series-parallel graphs with unit capacities. As main result, we formulate a greedy algorithm for MCDFP and provide a full characterization via forbidden subgraphs of the class of graphs, for which this greedy algorithm always yields an optimum solution (for arbitrary choices of problem parameters). G is a subclass of the class of two-terminal series-parallel graphs. We show that the greedy algorithm solves MCDFP restricted to graphs in G in polynomial time.

86 citations


Journal ArticleDOI
01 Aug 2004-Networks
TL;DR: This article surveys several broad classes of waiting policies and shows how techniques for speeding up dynamic programming can be effectively applied to obtain practical algorithms for these different problem variants.
Abstract: We study the problem of computing minimum-cost paths through a time-varying network, in which the travel time and travel cost of each arc are known functions of one's departure time along the arc. For some problem instances, the ability to wait at nodes may allow for less costly paths through the network. When waiting is allowed, it is constrained by a (potentially time-varying) waiting policy that describes the length of time one may wait and the cost of waiting at every node. In discrete time, time-dependent shortest path problems with waiting constraints can be optimally solved by straightforward dynamic programming algorithms; however, for some waiting policies these algorithms can be computationally impractical. In this article, we survey several broad classes of waiting policies and show how techniques for speeding up dynamic programming can be effectively applied to obtain practical algorithms for these different problem variants. © 2004 Wiley Periodicals, Inc. NETWORKS, Vol. 44(1), 41–46 2004

85 citations


Journal IssueDOI
01 Dec 2004-Networks
TL;DR: In this paper, the authors showed that all alternating group graphs are pan-connected, that is, every two vertices x and y in the graph are connected by a path of length k for each k satisfying dlx, yr ≤ k ≤ vVv - 1, where d lx, y denotes the distance between X and y, and vvv is the number of vertices in the network.
Abstract: Jwo et al. lNetworks 23 l1993r 315–326r introduced the alternating group graph as an interconnection network topology for computing systems. They showed that the proposed structure has many advantages over n-cubes and star graphs. For example, all alternating group graphs are hamiltonian-connected li.e., every pair of vertices in the graph are connected by a hamiltonian pathr and pancyclic li.e., the graph can embed cycles with arbitrary length with dilation 1r. In this article, we give a stronger result: all alternating group graphs are panconnected, that is, every two vertices x and y in the graph are connected by a path of length k for each k satisfying dlx, yr ≤ k ≤ vVv - 1, where dlx, yr denotes the distance between x and y, and vVv is the number of vertices in the graph. Moreover, we show that the r-dimensional alternating group graph AGr, r ≥ 4, is lr - 3r-vertex fault-tolerant Hamiltonian-connected and lr - 2r-vertex fault-tolerant hamiltonian. The latter result can be viewed as complementary to the recent work of Lo and Chen lIEEE Trans. Parallel and Distributed Systems 12 l2001r 209–222r, which studies the fault-tolerant hamiltonicity in faulty arrangement graphs. © 2004 Wiley Periodicals, Inc. NETWORKS, Vol. 44l4r, 302–310 2004

77 citations


Journal ArticleDOI
01 Sep 2004-Networks
TL;DR: In this article, a local search approach is proposed, and different metaheuristic algorithms, such as tabu search, iterated local search and random multistart, have been developed, based on such local search.
Abstract: This article deals with a Hub Location Problem arising in Telecommunication Network Design. The considered network presents two different kinds of nodes: access nodes, that represent source and destination of traffic demands but cannot be directly connected, and transit nodes, that have no own traffic demand but collect traffic from access nodes and route it through the network. Transit nodes are supposed to be fully connected. Given a set of access nodes and a set of potential locations for the transit nodes, the problem is to decide number and positions of the transit nodes to guarantee that all access nodes are allocated to a transit node, satisfying capacity constraints. The goal is to minimize the total cost of the network, which is the sum of connection costs and nodes fixed costs. The problem is a Hub Location Problem, which is known to be NP-hard. A local search approach is proposed, and different metaheuristic algorithms, such as tabu search, iterated local search and random multistart, have been developed, based on such local search. [A preliminary procedure has been developed in a research project joint with Telecom Italia (Turin Research & Innovation Laboratories) and a patent application has been filed to cover this issue.] © 2004 Wiley Periodicals, Inc. NETWOEKS, Vol. 44(2), 94–105 2004

75 citations


Journal ArticleDOI
01 Jan 2004-Networks
TL;DR: This work presents a novel linear mixed-integer mathematical formulation and two heuristic solution procedures for network design and routing for Internet Protocol lIPr traffic, using mixed- integer programming to generate a sequence of routing solutions.
Abstract: We consider network design and routing for Internet Protocol lIPr traffic. The design problem concerns capacity dimensioning of communication links, where the design cost consists of fixed charges and linear capacity expansion costs. The optimization problem also concerns determining the amount of traffic demand to be carried by the network and the metric used by a shortest path routing protocol. We present a novel linear mixed-integer mathematical formulation and two heuristic solution procedures. The first heuristic uses mixed-integer programming to generate a sequence of routing solutions. The second solution approach is a simulated annealing meta heuristic. Computational experiments for synthesized and real-life networks show that high-quality solutions can be obtained by both approaches. © 2003 Wiley Periodicals, Inc.

70 citations


Journal ArticleDOI
01 Sep 2004-Networks
TL;DR: A family of valid inequalities is derived that generalizes the facet defining inequalities and that can be separated in polynomial time.
Abstract: We consider two formulations for the uncapacitated hub location problem with single assignment (UHL), which use multicommodity flow variables. We project out the flow variables and determine some extreme rays of the projection cones. Then we investigate whether the corresponding inequalities define facets of the UHL polyhedron. We also present two families of facet defining inequalities that dominate some projection inequalities. Finally, we derive a family of valid inequalities that generalizes the facet defining inequalities and that can be separated in polynomial time. © 2004 Wiley Periodicals, Inc. NETWORKS, Vol. 44(2), 84–93 2004

65 citations


Journal ArticleDOI
01 Sep 2004-Networks
TL;DR: A variant of the classical VNS scheme that is intended to be of high generality, but exploits the specific structure of some MIPs where the set of binary variables partitions naturally into two levels, with the property that fixing the value of the first‐level variables produces an easier‐to‐solve subproblem.
Abstract: Eective heuristic solution methods for general Mixed-Integer Programs (MIPs) are strongly required in many practical applications, and have been the subject of an intensive research eort in the recent years. Fischetti and Lodi [6] recently proposed an exact solution technique based on the use of branching conditions expressed through (invalid) linear inequalities called local branching cuts. In the concluding remarks of their paper, these authors anticipated the possibility their method be used to design a genuine MIP metaheuristic framework akin to Tabu Search (TS) or Variable Neighborhood Search (VNS), based on an external MIP solver. In the present paper we introduce and analyze computationally a specific implementation of the above idea. In particular, we address MIPs with binary variables, and propose a variant of the classical VNS scheme that we call Diversification, Refining, and Tight-refining (DRT). The new approach is intended to be of high generality, but exploits the specific structure of some MIPs where the set of binary variables partitions naturally into two levels, with the property that fixing the value of the first-level variables produces an easier-to-solve (but still hard) subproblem. This is often the case, e.g., in hard facility location problems arising in telecommunication network design. Our method detects automatically the presence in the MIP model of the first-level binary variables, if any, according to simple heuristic criteria. This information is then exploited during the intensification phase of the local search, so as to explore nested solution neighborhoods defined by local branching cuts aecting

59 citations


Journal ArticleDOI
Tetsuya Fujie1
01 Jul 2004-Networks
TL;DR: An integer programming approach to the Maximum Leaf Spanning Tree Problem is considered and the facial structure of polytopes arising from the formulations are studied.
Abstract: The Maximum Leaf Spanning Tree Problem (MLSTP) is to find a spanning tree in a given undirected graph, whose number of leaves (vertices of degree 1) is maximum. In this article, we consider an integer programming approach to the MLSTP. We provide two formulations of the MLSTP and study the facial structure of polytopes arising from the formulations. Moreover, several relaxation problems are compared. © 2004 Wiley Periodicals, Inc.

Journal ArticleDOI
01 Oct 2004-Networks
TL;DR: This work estimates and characterize the edge congestion‐sum measure for embeddings of various graphs such as cycles, wheels, and generalized wheels into arbitrary trees and produces optimal values of sum of dilations and sum of edge‐congestions in linear time.
Abstract: We estimate and characterize the edge congestion-sum measure for embeddings of various graphs such as cycles, wheels, and generalized wheels into arbitrary trees. All embedding algorithms apply an interesting general technique based on the consecutive label property. Our algorithms produce optimal values of sum of dilations and sum of edge-congestions in linear time. © 2004 Wiley Periodicals, Inc. NETWORKS, Vol. 44(3), 173–178 2004

Journal ArticleDOI
Timothy Y. Chow, Philip J. Lin1
01 Oct 2004-Networks
TL;DR: In this paper, the authors studied the problem of minimizing the number of bidirectional SONET rings required to support a given traffic demand, and showed that the linear programming relaxation is not within a constant factor of the optimum.
Abstract: The problem of minimizing the number of bidirectional SONET rings required to support a given traffic demand has been studied by several researchers. Here we study the related ring-grooming problem of minimizing the number of add/drop locations instead of the number of rings; in a number of situations this is a better approximation to the true equipment cost. Our main result is a new lower bound for the case of uniform traffic. This allows us to prove that a certain simple algorithm for uniform traffic is, in fact, a constant-factor approximation algorithm, and it also demonstrates that known lower bounds for the general problem—in particular, the linear programming relaxation—are not within a constant factor of the optimum. We also show that our results for uniform traffic extend readily to the more practically important case of quasi-uniform traffic. Finally, we show that if the number of nodes on the ring is fixed, then ring grooming is solvable in polynomial time; however, whether ring grooming is fixed-parameter tractable is still an open question. © 2004 Wiley Periodicals, Inc. NETWORKS, Vol. 44(3), 194 –202 2004

Journal ArticleDOI
01 Jul 2004-Networks
TL;DR: It is proved that if the function f is crossing supermodular, then any basic solution of the LP relaxation of the problem contains at least one variable with value greater or equal to ¼, which implies a 4‐approximation algorithm for the class of directed network design problems.
Abstract: We present approximation algorithms for a class of directed network design problems. The network design problem is to find a minimum cost subgraph such that for each vertex set S there are at least f(S) arcs leaving the set S. In the last 10 years general techniques have been developed for designing approximation algorithms for undirected network design problems. Recently, Kamal Jain gave a 2-approximation algorithm for the case when the function f is weakly supermodular. There has been very little progress made on directed network design problems. The main techniques used for the undirected problems do not have simple extensions to the directed case. Andras Frank has shown that in a special case when the function f is intersecting supermodular the problem can be solved optimally. In this article, we use this result to get a 2-approximation algorithm for a more general case when f is crossing supermodular. We also extend Jain's techniques to directed problems. We prove that if the function f is crossing supermodular, then any basic solution of the LP relaxation of our problem contains at least one variable with value greater or equal to ¼. This result implies a 4-approximation algorithm for the class of directed network design problems. © 2004 Wiley Periodicals, Inc.

Journal ArticleDOI
01 Mar 2004-Networks
TL;DR: This article presents a branch‐and‐cut algorithm for the Generalized Minimum Spanning Tree Problem (GMSTP), given an undirected graph whose vertex set is partitioned into clusters, which consists of determining a minimum‐cost tree including exactly one vertex per cluster.
Abstract: This article presents a branch-and-cut algorithm for the Generalized Minimum Spanning Tree Problem (GMSTP). Given an undirected graph whose vertex set is partitioned into clusters, the GMSTP consists of determining a minimum-cost tree including exactly one vertex per cluster. Applications of the GMSTP are encountered in telecommunications. An integer linear programming formulation is presented and new classes of valid inequalities are developed, several of which are proved to be facet-defining. A branch-and-cut algorithm and a tabu search heuristic are developed. Extensive computational experiments show that instances involving up to 160 or 200 vertices can be solved to optimality, depending on whether edge costs are Euclidean or random. © 2004 Wiley Periodicals, Inc.

Journal ArticleDOI
01 Jul 2004-Networks
TL;DR: All their embeddings have load 1 and dilation 1 and when such an embedding f : V(G) 3 V(H) exists, the authors say that G is a subgraph of H and write G H.
Abstract: ding with smallest load and dilation. Clearly, an embedding f : V(G) 3 V(H) with load 1 and dilation 1 is an optimal embedding. In this case, f is 1 1 and preserves adjacency, so G is isomorphic to a subgraph of H. In this article, all our embeddings have load 1 and dilation 1. Moreover, when such an embedding f : V(G) 3 V(H) exists, we say that G is a subgraph of H and write G H.

Journal ArticleDOI
01 May 2004-Networks
TL;DR: Two integer programming models for the 2‐path network problem are presented and properties of associated polytopes, including cutting planes, are studied.
Abstract: Given a graph with nonnegative edge weights and a set D of node pairs, the 2-path network problem requires a minimum weight set of edges such that the induced subgraph contains a path with one or two edges connecting each pair in D. The problem is NP-hard. We present two integer programming models for the problem and study properties of associated polytopes, including cutting planes. Two approximation algorithms are suggested and analyzed. Some computational experience is reported. © 2004 Wiley Periodicals, Inc.

Journal ArticleDOI
01 Mar 2004-Networks
TL;DR: This is the first algorithm for gossiping in this model whose running time is only a polylogarithmic factor away from the optimum, and the fastest previously known algorithm for this problem works in time O(n3/2log2n).
Abstract: We present an O(n log4n)-time randomized algorithm for gossiping in radio networks with unknown topology. This is the first algorithm for gossiping in this model whose running time is only a polylogarithmic factor away from the optimum. The fastest previously known (deterministic) algorithm for this problem works in time O(n3/2log2n). © 2004 Wiley Periodicals, Inc.

Journal IssueDOI
01 Dec 2004-Networks
TL;DR: In this article, the authors presented an alternative model for the situation when the tree diameter D is odd and showed that the linear programming gaps for the tightened model are very small, typically less than 0.5p and are usually one third to one tenth of the gaps of the best previous model described in Gouveia and Magnanti l2003r.
Abstract: In a previous article, using underlying graph theoretical properties, Gouveia and Magnanti l2003r described several network flow-based formulations for diameter-constrained tree problems. Their computational results showed that, even with several enhancements, models for situations when the tree diameter D is odd proved to be more difficult to solve than those when D is even. In this article we provide an alternative modeling approach for the situation when D is odd. The approach views the diameter-constrained minimum spanning tree as being composed of a variant of a directed spanning tree lfrom an artificial root noder together with two constrained paths, a shortest and a longest path, from the root node to any node in the tree. We also show how to view the feasible set of the linear programming relaxation of the new formulation as the intersection of two integer polyhedra, a so-called triangle-tree polyhedron and a constrained path polyhedron. This characterization improves upon a model of Gouveia and Magnanti l2003r whose linear programming relaxation feasible set is the intersection of three rather than two integer polyhedra. The linear programming gaps for the tightened model are very small, typically less than 0.5p, and are usually one third to one tenth of the gaps of the best previous model described in Gouveia and Magnanti l2003r. Moreover, using the new model, we have been able to solve large Euclidean problem instances that are not solvable by the previous approaches. © 2004 Wiley Periodicals, Inc.

Journal ArticleDOI
01 Jul 2004-Networks
TL;DR: A mixed‐integer programming model, in which sufficient slack is explicitly introduced on the directed cycles of the network while flow routing decisions are made, which gives strong valid inequalities that use the survivability requirements.
Abstract: A network is said to be survivable if it has sufficient capacity for rerouting all of its flow under the failure of any one of its edges. Here, we present a polyhedral approach for designing survivable networks. We describe a mixed-integer programming model, in which sufficient slack is explicitly introduced on the directed cycles of the network while flow routing decisions are made. In case of a failure, flow is rerouted along the slacks reserved on directed cycles. We give strong valid inequalities that use the survivability requirements. We present a computational study with a column-and-cut generation algorithm for designing capacitated survivable networks. © 2004 Wiley Periodicals, Inc.

Journal ArticleDOI
01 Jan 2004-Networks
TL;DR: The algorithm that is presented follows the general framework for such an algorithm sketched by Robertson and Seymour with the addition of pruning techniques for runtime speedup.
Abstract: Given a simple graph G, a simple connected graph H, and a branch decomposition of G of width k, we present a practical algorithm to test if H is a minor of G. The notion of branch decompositions and its related connectivity invariant for graphs, branchwidth, were introduced by Robertson and Seymour. The algorithm that we present follows the general framework for such an algorithm sketched by Robertson and Seymour with the addition of pruning techniques for runtime speedup. © 2003 Wiley Periodicals, Inc.

Journal ArticleDOI
01 Aug 2004-Networks
TL;DR: Stochastic integer programming techniques tailored toward solving a Synchronous Optical Network (SONET) ring design problem with uncertain demands are developed, and a nonlinear reformulation of the model can be used to capture an exponential number of optimality cuts generated by the linear model.
Abstract: We develop stochastic integer programming techniques tailored toward solving a Synchronous Optical Network (SONET) ring design problem with uncertain demands. Our approach is based on an L-shaped algorithm, whose (integer) master program prescribes a candidate network design, and whose (continuous) subproblems relay information regarding potential shortage penalty costs to the ring design decisions. This naive implementation performs very poorly due to two major problems: (1) the weakness of the master problem relaxations, and (2) the limited information passed to the master problem by the optimality cuts. Accordingly, we enforce certain necessary conditions regarding shortage penalty contributions to the objective function within the master problem, along with a corresponding set of valid inequalities that improves the solvability of the master problem. We also show how a nonlinear reformulation of the model can be used to capture an exponential number of optimality cuts generated by the linear model. We augment these techniques with a powerful upper-bounding heuristic to further accelerate the convergence of the algorithm, and demonstrate the effectiveness of our methodologies on a test bed of randomly generated stochastic SONET instances. © 2004 Wiley Periodicals, Inc. NETWORKS, Vol. 44(1), 12–26 2004

Journal ArticleDOI
01 Jan 2004-Networks
TL;DR: A family of new mixed-integer programming formulations whose associated linear programming relaxations can be tighter than that of the usual cutset formulation are presented, which motivate several SND combinatorial heuristics and facilitate the analysis of their worst-case performance.
Abstract: The survivable network design lSNDr problem seeks a minimum-cost robust network configuration that provides a specified number of alternate ledge-disjointr paths between nodes of the network. For this problem, we present a family of new mixed-integer programming formulations whose associated linear programming relaxations can be tighter than that of the usual cutset formulation. The new formulations, called connectivity-splitting models, strengthen the cutset formulation by splitting the connectivity requirements across critical cutsets lwith crossing requirements of at least twor into two separate requirements and strengthening the connectivity constraints across regular cutsets lwith crossing requirements of oner. As special cases of this broad modeling approach, we obtain three intuitive versions of the model. A connectivity-peeling version peels off the lowest connectivity level, a connectivity-dividing version divides the connectivity requirements for all critical cutsets, and an access-completion version separates the design decisions for critical cutsets from those for regular cutsets. These stronger formulations motivate several SND combinatorial heuristics and facilitate the analysis of their worst-case performance. Our bounds on the heuristic costs relative to the optimal values of the integer program and the linear programming relaxation of our tighter formulation are stronger than some previously known performance bounds for combinatorial heuristics. © 2003 Wiley Periodicals, Inc.

Journal ArticleDOI
01 Sep 2004-Networks
TL;DR: This article investigates a two‐user competitive scheduling problem in a Universal Mobile Telecommunication System developed within the European IST project FUTURE, and proposes a fast lagrangian heuristic able to cope with a severe real‐time requirement.
Abstract: This article investigates a two-user competitive scheduling problem. The problem arises in a Universal Mobile Telecommunication System (UMTS) developed within the European IST project FUTURE: given two mobile terminals, one wants to maximize the on-time data packets transmitted to one user, while guaranteeing a certain amount of on-time data packets to the other. We show that the problem is NP-hard, despite peculiar properties of data and solutions. We propose a fast lagrangian heuristic able to cope with a severe real-time requirement, and compare it to a greedy-like heuristic on a set of practical instances. © 2004 Wiley Periodicals, Inc. NETWORKS, Vol. 44(2), 132–141 2004

Journal ArticleDOI
01 Oct 2004-Networks
TL;DR: The analysis indicates that the degree of an optimal subgraph for each of the problems above is well estimated by certain polynomially solvable linear programs, which suggests that the linear programs described could be useful in obtaining optimal solutions via branch and bound.
Abstract: We give quasipolynomial-time approximation algorithms for designing networks with a minimum degree. Using our methods, one can design networks whose connectivity is specified by “proper” functions, a class of 0–1 functions indicating the number of edges crossing each cut. We also provide quasipolynomial-time approximation algorithms for finding two-edge-connected spanning subgraphs of approximately minimum degree of a given two-edge-connected graph, and a spanning tree (branching) of approximately minimum degree of a directed graph. The degree of the output network in all cases is guaranteed to be at most (1 + ϵ) times the optimal degree, plus an additive O(log1+ϵn) for any ϵ > 0. Our analysis indicates that the degree of an optimal subgraph for each of the problems above is well estimated by certain polynomially solvable linear programs. This suggests that the linear programs we describe could be useful in obtaining optimal solutions via branch and bound. © 2004 Wiley Periodicals, Inc. NETWORKS, Vol. 44(3), 203–215 2004

Journal ArticleDOI
01 May 2004-Networks
TL;DR: A new complete (exact) algorithm is proposed for solving traffic engineering's routing task, which is a hybrid that tightly integrates Lagrangian optimization and Constraint Programming search, and it is revealed that the hybrid algorithm typically yields the most informative results in the most effective way.
Abstract: Traffic engineering seeks to route traffic demands in data networks to guarantee certain quality of service (QoS) parameters while efficiently utilizing network resources. MPLS, for example, provides the essential capabilities to achieve this with explicit routing. Finding paths for all the demands which meet QoS requirements is a nontrivial task. Indeed, guaranteeing just bandwidth is known to be -hard. In this paper, we propose a new complete (exact) algorithm for solving this problem, which is a hybrid that tightly integrates Lagrangian optimization and Constraint Programming search. We evaluate its performance on a set of benchmark tests, based on a large well-provisioned commercial backbone. The tests involve demand sets of varying size, mostly between 100 and 600 demands. We compare the results with those achieved by several other well-known algorithms, some complete and some heuristic. This reveals that the hybrid algorithm typically yields the most informative results in the most effective way. It resolves most of the test cases either by finding a solution or by proving infeasibility, each taking only a few seconds. Moreover, the solutions found for solvable problems are provably near-optimal. The results show, perhaps surprisingly, that the routing task can be difficult even in a very well-provisioned network. © 2004 Wiley Periodicals, Inc.

Journal ArticleDOI
01 Mar 2004-Networks
TL;DR: This paper presents a new algorithm for finding an absolute center (minimax criterion) of an undirected network with n nodes and m arcs based on the concept of minimum‐diameter trees that synthesizes and generalizes some well‐known results in this area.
Abstract: This paper presents a new algorithm for finding an absolute center (minimax criterion) of an undirected network with n nodes and m arcs based on the concept of minimum-diameter trees. Local centers and their associated radii are identified by a monotonically increasing sequence of lower bounds on the radii. Computational efficiency is addressed in terms of worst-case complexity and practical performance. The complexity of the algorithm is 0(n2 lg n + mn). In practice, because of its very rapid convergence, the algorithm renders the problem amenable even to manual solution for quite large networks, provided that the minimal-distance matrix is given. Otherwise, evaluation of this matrix is the effective computational bottleneck. An interesting feature of the algorithm and its theoretical foundations is that it synthesizes and generalizes some well-known results in this area, particularly Halpern's lower bound on the local radius of a network and properties of centers of tree networks. © 2004 Wiley Periodicals, Inc.

Journal ArticleDOI
01 Sep 2004-Networks
TL;DR: The Dantzig-Wolfe (DW) decomposition as an approach for solving the MINREV problem is investigated and its relationships with a cutting plane algorithm and other proposed approaches are established.
Abstract: The objective of the minimum toll revenue (MINREV) problem is to find tolls that simultaneously cause users to use the transportation network efficiently and minimize the total toll revenues that must be collected. This article investigates the Dantzig-Wolfe (DW) decomposition as an approach for solving the MINREV problem and establishes its relationships with a cutting plane algorithm and other proposed approaches. The article also identifies the variant of DW decomposition most suitable for implementation. Numerical experiments with real transportation networks suggest that DW decomposition is robust and should be used when the problems are too large for standard linear programming software. Although transportation planning is the application emphasized in this article, it should be noted that the MINREV problem also has applications in telecommunication network design and control. © 2004 Wiley Periodicals, Inc. NETWORKS, Vol. 44(2), 142–150 2004

Journal ArticleDOI
01 Aug 2004-Networks
TL;DR: Analysis of special cases where a solution is determined by solving deterministic versions of the problems and efficient algorithms to solve the problems in general are included.
Abstract: In this article we consider four models for locating a facility on an undirected network with demand weights, which are independent discrete random variables. These problems include the probabilistic versions of two models for locating desirable facilities: the 1-median and 1-minimax problems and two problems for locating undesirable facilities: the 1-antimedian and 1-maximin problems. The article contains analysis of special cases where a solution is determined by solving deterministic versions of the problems and efficient algorithms to solve the problems in general. © 2004 Wiley Periodicals, Inc. NETWORKS, Vol. 44(1), 47–57 2004

Journal ArticleDOI
01 Sep 2004-Networks
TL;DR: Two on‐line rectangle packing algorithms are proposed with the objective of maximizing the system efficiency and are compared with those of known algorithms on benchmark instances for rectangle packing.
Abstract: The Grid computing paradigm is originated from a new computing infrastructure for scientific research and cooperation, and is becoming an established technology for large-scale resource sharing and distributed integration. Two main problems arise: how to efficiently allocate resources to tasks and, after this, how to schedule them. In this article we propose to solve the scheduling phase by means of rectangle packing algorithms. In particular, two on-line rectangle packing algorithms are proposed with the objective of maximizing the system efficiency. A wide computational analysis is provided. The performances of the proposed algorithms are first compared with those of known algorithms on benchmark instances for rectangle packing, and then are evaluated on different Grid scheduling scenarios associated with different processing and dataset environments.