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CostDistance: Two Metric Network Design
 In Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science
, 2000
"... Abstract We present the CostDistance problem: finding a Steiner tree which optimizes the sum of edge costs along one metric and the sum of sourcesink distances along an unrelated second metric. We give the first known O(log k) randomized approximation scheme for CostDistance, where k is the numbe ..."
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Abstract We present the CostDistance problem: finding a Steiner tree which optimizes the sum of edge costs along one metric and the sum of sourcesink distances along an unrelated second metric. We give the first known O(log k) randomized approximation scheme for CostDistance, where k is the number of sources. We reduce many common network design problems to CostDistance, obtaining (in some cases) the first known logarithmic approximation for them. These problems include singlesink buyatbulk with variable pipe types between different sets of nodes, facility location with buyatbulk type costs on edges, and maybecast with combind cost and distance metrics. Our algorithm is also the algorithm of choice for several previous network design problems, due to its ease of implementation and fast running time. 1 Introduction Consider designing a network from the ground up. We are given a set of customers, and need to place various servers and network links in order to cheaply provide sufficient service. If we only need to place the servers, this becomes the facility location problem and constantapproximations are known. If a single server handles all customers, and we impose the additional constraint that the set of available network link types is the same for every pair of nodes (subject to constant scaling factors on cost) then this is the single sink buyatbulk problem. We give the first known approximation for the general version of this problem with both servers and network links. We reduce the network design problem to an elegant theoretical framework: the CostDistance problem. We are given a graph with a single distinguished sink node (server). Every edge in this graph can be measured along two metrics; the first will be called cost and the second will be length. Note that the two metrics are entirely independent, and that there may be any number of parallel edges in the graph. We are given a set of sources (customers). Our objective is to construct a Steiner tree connecting the sources to the sink while minimizing the combined sum of the cost of the edges in the tree and sum over sources of the weighted length from source to sink.
A 3Approximation Algorithm for the kLevel Uncapacitated Facility Location Problem
 Information Processing Letters
, 1999
"... In the klevel uncapacitated facility location problem, we have a set of demand points where clients are located. The demand of each client is known. Facilities have to be located at given sites in orde to service the clients, and each client is to be serviced by a sequence of k different facilit ..."
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Cited by 34 (1 self)
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In the klevel uncapacitated facility location problem, we have a set of demand points where clients are located. The demand of each client is known. Facilities have to be located at given sites in orde to service the clients, and each client is to be serviced by a sequence of k different facilities, each of which belongs to a distinct level. Thee are no capacity restrictions on the facilities. There is a positive fixed cost of setting up a facility, and a pe unit cost of shipping goods between each pair of locations. We assume that these distances are all nonnegative and satisfy the triangle inequality. The problem is to find an assignment of each client to a sequence of k facilities, one at each level, so that the demand of each client is satisfied, for which the sum of the setup costs and the service costs is minimized.
Approximating the TwoLevel Facility Location Problem Via a QuasiGreedy Approach
 IN PROCEEDINGS OF THE 15TH ANNUAL ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS (SODA
, 2004
"... We propose a quasigreedy algorithm for approximating the classical uncapacitated 2level facility location problem (2LFLP). Our algorithm, unlike the standard greedy algorithm, selects a suboptimal candidate at each step. It also relates the minimization 2LFLP problem, in an interesting way, ..."
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Cited by 18 (1 self)
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We propose a quasigreedy algorithm for approximating the classical uncapacitated 2level facility location problem (2LFLP). Our algorithm, unlike the standard greedy algorithm, selects a suboptimal candidate at each step. It also relates the minimization 2LFLP problem, in an interesting way, to the maximization version of the single level facility location problem. Another feature of our algorithm is that it combines the technique of randomized rounding with that of dual fitting. This new approach
On the TwoLevel Uncapacitated Facility Location Problem
 INFORMS J. COMPUT
, 1996
"... We study the twolevel uncapacitated facility location (TUFL) problem. Given two types of facilities, which we call yfacilities and zfacilities, the problem is to decide which facilities of both types to open, and to which pair of y and zfacilities each client should be assigned, in order to sat ..."
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Cited by 18 (3 self)
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We study the twolevel uncapacitated facility location (TUFL) problem. Given two types of facilities, which we call yfacilities and zfacilities, the problem is to decide which facilities of both types to open, and to which pair of y and zfacilities each client should be assigned, in order to satisfy the demand at maximum profit. We first present two multicommodity flow formulations of TUFL and investigate the relationship between these formulations and similar formulations of the onelevel uncapacitated facility location (UFL) problem. In particular, we show that all nontrivial facets for UFL define facets for the twolevel problem, and derive conditions when facets of TUFL are also facets for UFL. For both formulations of TUFL, we introduce new families of facets and valid inequalities and discuss the associated separation problems. We also characterize the extreme points of the LPrelaxation of the first formulation. While the LPrelaxation of a multicommodity formulation provi...
A Genetic Algorithm for the Index Selection Problem
 In Applications of Evolutionary Computing
, 2003
"... This paper considers the problem of minimizing the response time for a given database workload by a proper choice of indexes. This problem is NPhard and known in the literature as the Index Selection Problem (ISP). ..."
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Cited by 10 (0 self)
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This paper considers the problem of minimizing the response time for a given database workload by a proper choice of indexes. This problem is NPhard and known in the literature as the Index Selection Problem (ISP).
Location Problems Optimization by a SelfOrganizing Multiagent Approach
, 2009
"... The Facility Location Problem (FLP) requires locating facilities in order to optimize some performance criteria. This problem occurs in many practical settings where facilities provide a service, such as the location of plants, busstops, fire stations, etc. Particularly, we deal with the continuo ..."
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The Facility Location Problem (FLP) requires locating facilities in order to optimize some performance criteria. This problem occurs in many practical settings where facilities provide a service, such as the location of plants, busstops, fire stations, etc. Particularly, we deal with the continuous version of location problem where facilities have to be located in an Euclidean plane. This paper contributes to research on location problems by exploring a new approach based on reactive multiagent systems. The proposed model relies on a set of agents situated in a common environment which interact and attempt to reach a global optimization goal. The interactions between agents and their environment, which are based on the artificial potential fields approach, allow to locally optimize the agent’s locations. The optimization of the whole system is the outcome of a process of agents selforganization. Then, we present how the model can be extended to the multilevel version of the location problem. Finally, the approach is evaluated to check its relevance. These evaluations concern both presented versions of the location problem.
Facility Location: Discrete Models and Local Search Methods
"... Abstract.Discrete location theory is one of the most dynamic areas of operations research. We present the basic mathematical models used in this field, as well as their properties and relationship with pseudoBoolean functions. We also investigate the theory of PLScomplete problems, average and wo ..."
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Cited by 3 (2 self)
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Abstract.Discrete location theory is one of the most dynamic areas of operations research. We present the basic mathematical models used in this field, as well as their properties and relationship with pseudoBoolean functions. We also investigate the theory of PLScomplete problems, average and worst case computational complexity of the local search algorithms, and approximate local search. Finally, we discuss computationally difficult test instances and promising directions for further research.
Approximation Algorithms for Concave Cost Network Flow Problems
, 2003
"... The cost structures for resource allocation in many network design problems obey economies of scale, meaning that the cost per unit resource becomes cheaper as the amount of resources allocated increases. For instance, if we are purchasing cables to route data in a network, the cost per unit bandwid ..."
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Cited by 3 (0 self)
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The cost structures for resource allocation in many network design problems obey economies of scale, meaning that the cost per unit resource becomes cheaper as the amount of resources allocated increases. For instance, if we are purchasing cables to route data in a network, the cost per unit bandwidth reduces as the bandwidth we need to route increases. Another feature of resource allocation is granularity, meaning that the resource can only be purchased in multiples of a certain minimum quantity. Again, in the context of purchasing cables in a network, the minimum capacity cable available might be a T1 line with capacity 1 Mbps. In this