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A MultiExchange Local Search Algorithm for the Capacitated Facility Location Problem
 Mathematics of Operations Research
, 2004
"... We present a multiexchange local search algorithm for approximating the capacitated facility location problem (CFLP), where a new local improvement operation is introduced that possibly exchanges multiple facilities simultaneously. We give a tight analysis for our algorithm and show that the per ..."
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Cited by 35 (0 self)
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We present a multiexchange local search algorithm for approximating the capacitated facility location problem (CFLP), where a new local improvement operation is introduced that possibly exchanges multiple facilities simultaneously. We give a tight analysis for our algorithm and show that the performance guarantee of the algorithm is between 3+ 2 # 2 # and 3+ 2 # 2+ # for any given constant # > 0. Previously known best approximation ratio for the CFLP is 7.88, due to Mahdian and Pal (2003), based on the operations proposed by Pal, Tardos and Wexler (2001).
LPbased approximation algorithms for capacitated facility location
 in Proc. of IPCO’04, 2004
"... In the capacitated facility location problem with hard capacities, we are given a set of facilities, F, and a set of clients D in a common metric space. Each facility i has a facility opening cost fi and capacity ui that specifies the maximum number of clients that may be assigned to this facility. ..."
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Cited by 24 (1 self)
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In the capacitated facility location problem with hard capacities, we are given a set of facilities, F, and a set of clients D in a common metric space. Each facility i has a facility opening cost fi and capacity ui that specifies the maximum number of clients that may be assigned to this facility. We want to open some facilities from the set F and assign each client to an open facility so that at most ui clients are assigned to any open facility i. The cost of assigning client j to facility i is given by the distance cij, and our goal is to minimize the sum of the facility opening costs and the client assignment costs. The only known approximation algorithms that deliver solutions within a constant factor of optimal for this NPhard problem are based on local search techniques. It is an open problem to devise an approximation algorithm for this problem based on a linear programming lower bound (or indeed, to prove a constant integrality gap for any LP relaxation). We make progress on this question by giving a 5approximation algorithm for the special case in which all of the facility costs are equal, by rounding the optimal solution to the standard LP relaxation. One notable aspect of our algorithm is that it relies on partitioning the input into a collection of singledemand capacitated facility location problems, approximately solving them, and then combining these solutions in a natural way.
Distributed placement of service facilities in largescale networks
, 2006
"... Abstract — The effectiveness of service provisioning in largescale networks is highly dependent on the number and location of service facilities deployed at various hosts. The classical, centralized approach to determining the latter would amount to formulating and solving the uncapacitated kmedian ..."
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Cited by 23 (3 self)
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Abstract — The effectiveness of service provisioning in largescale networks is highly dependent on the number and location of service facilities deployed at various hosts. The classical, centralized approach to determining the latter would amount to formulating and solving the uncapacitated kmedian (UKM) problem (if the requested number of facilities is fixed), or the uncapacitated facility location (UFL) problem (if the number of facilities is also to be optimized). Clearly, such centralized approaches require knowledge of global topological and demand information, and thus do not scale and are not practical for large networks. The key question posed and answered in this paper is the following: “How can we determine in a distributed and scalable manner the number and location of service facilities?” We propose an innovative approach in which topology and demand information is limited to neighborhoods, or balls of small radius around selected facilities, whereas demand information is captured implicitly for the remaining (remote) clients outside these neighborhoods, by mapping them to clients on the edge of the neighborhood; the ball radius regulates the tradeoff between scalability and performance. We develop a scalable, distributed approach that answers our key question through an iterative reoptimization of the location and the number of facilities within such balls. We show that even for small values of the radius (1 or 2), our distributed approach achieves performance under various synthetic and real Internet topologies that is comparable to that of optimal, centralized approaches requiring full topology and demand information.
Improved Approximation for Universal Facility Location
"... The Universal Facility Location problem (UniFL) is a generalized formulation which contains several variants of facility location including capacitated facility location (1CFL) as its special cases. We present a 6 + ~ approximation for the UniFL problem, thus improving the 8 % e approximation giv ..."
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Cited by 12 (0 self)
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The Universal Facility Location problem (UniFL) is a generalized formulation which contains several variants of facility location including capacitated facility location (1CFL) as its special cases. We present a 6 + ~ approximation for the UniFL problem, thus improving the 8 % e approximation given by iVlahdian and Pal. Our result bridges the existing gap between the UniFL problem and the 1CFL problem.
LowerBounded Facility Location
 SODA 2008
, 2008
"... We study the lowerbounded facility location problem, which generalizes the classical uncapacitated facility location problem in that it comes with lower bound constraints for the number of clients assigned to a facility in the case that this facility is opened. This problem was introduced independe ..."
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We study the lowerbounded facility location problem, which generalizes the classical uncapacitated facility location problem in that it comes with lower bound constraints for the number of clients assigned to a facility in the case that this facility is opened. This problem was introduced independently in the papers by Karger and Minkoff [12] and by Guha, Meyerson, and Munagala [7], both of which give bicriteria approximation algorithms for it. These bicriteria algorithms come within a constant factor of the optimal solution cost, but they also violate the lower bound constraints by a constant factor. Our result in this paper is the first true approximation algorithm for the lowerbounded facility location problem, which respects the lower bound constraints and achieves a constant approximation ratio for the objective function. The main technical idea for the design of the algorithm is a reduction to the capacitated facility location problem, which has known constantfactor approximation algorithms. 1
The assignment problem in content distribution networks: Unsplittable hardcapacitated facility location
 in Proc. of ACMSIAM SODA
, 2009
"... In a Content Distribution Network (CDN), there are m servers storing the data; each of them has a specific bandwidth. All the requests from a particular client should be assigned to one server, because of the routing protocol used. The goal is to minimize the total cost of these assignments —cost of ..."
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Cited by 9 (4 self)
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In a Content Distribution Network (CDN), there are m servers storing the data; each of them has a specific bandwidth. All the requests from a particular client should be assigned to one server, because of the routing protocol used. The goal is to minimize the total cost of these assignments —cost of each is proportional to the distance as well as the request size — while the load on each server is kept below its bandwidth limit. When each server also has a setup cost, this is an unsplittable hardcapacitated facility location problem. As much attention as facility location problems have received, there has been no nontrivial approximation algorithm when we have hard capacities (i.e., there can only be one copy of each facility whose capacity cannot be violated) and demands are unsplittable (i.e., all the demand from a client has to be assigned to a single facility). We observe it is NPhard to approximate the cost to within any bounded factor. Thus, for an arbitrary constant ɛ> 0, we relax the capacities to a 1 + ɛ factor. For the case where capacities are almost uniform, we give a bicriteria O(log n, 1+ɛ)approximation algorithm for general metrics and a (1 + ɛ, 1 + ɛ)approximation algorithm for tree metrics. A bicriteria (α, β)approximation algorithm produces a solution of cost at most α times the optimum, while violating the capacities by no more than a β factor. We can get the same guarantee for nonuniform capacities if we allow quasipolynomial running time. In our algorithm, some clients guess the facility they are assigned to, and facilities decide the size of the clients they serve. A straightforward approach results in exponential running time. When costs do not satisfy metricity, we show that a 1.5 violation of capacities is necessary to obtain any approximation. It is worth noting that our results generalize bin packing (zero cost matrix and facility costs equal to one), knapsack (single facility with all costs being zero), minimum makespan scheduling for related machines (all costs being zero) and some facility location problems. Key words: approximation algorithm, PTAS, network, facility location
Minimizing movement in mobile facility location problems
 In FOCS 2008
"... In the mobile facility location problem, which is a variant of the classical facility location and kmedian problems, each facility and client is assigned to a start location in a metric graph and our goal is to find a destination node for each client and facility such that every client is sent to a ..."
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Cited by 9 (0 self)
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In the mobile facility location problem, which is a variant of the classical facility location and kmedian problems, each facility and client is assigned to a start location in a metric graph and our goal is to find a destination node for each client and facility such that every client is sent to a node which is the destination of some facility. The quality of a solution can be measured either by the total distance clients and facilities travel or by the maximum distance traveled by any client or facility. As we show in this paper (by an approximation preserving reduction), the problem of minimizing the total movement of facilities and clients generalizes the classical kmedian problem. The class of movement problems was introduced by Demaine et al. in SODA 2007 [8], where it was observed q simple 2approximation for the minimum maximum movement mobile facility location while an approximation for the minimum total movement variant and hardness results for both were left as open problems. Our main result here is an 8approximation algorithm for the minimum total movement mobile facility location problem. Our algorithm is obtained by rounding an LP relaxation in five phases. For the minimum maximum movement mobile facility location problem, we show that we cannot have a better than a 2approximation for the problem, unless P = NP; so the simple algorithm observed in [8] is essentially best possible. 1
Adding Capacity Points to a Wireless Mesh Network Using Local Search
"... Abstract — Wireless mesh network deployments are popular as a costeffective means to provide broadband connectivity to large user populations. As the network usage grows, network planners need to evolve an existing mesh network to provide additional capacity. In this paper, we study the problem of ..."
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Cited by 8 (1 self)
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Abstract — Wireless mesh network deployments are popular as a costeffective means to provide broadband connectivity to large user populations. As the network usage grows, network planners need to evolve an existing mesh network to provide additional capacity. In this paper, we study the problem of adding new capacity points (e.g., gateway nodes) to an existing mesh network. We first present a new technique for calculating gatewaylimited fair capacity as a function of the contention at each gateway. Then, we present two online gateway placement algorithms that use local search operations to maximize the capacity gain on an existing network. A key challenge is that each gateway’s capacity depends on the locations of other gateways and cannot be known in advance of determining a gateway placement. We address this challenge with two placement algorithms with different approaches to estimating the unknown gateway capacities. Our first placement algorithm, MinHopCount, is adapted from a solution to the facility location problem. MinHopCount minimizes path lengths and iteratively estimates the wireless capacity of each gateway location. Our second algorithm, MinContention, is adapted from a solution to the uncapacitated kmedian problem and minimizes average contention on mesh nodes, i.e. the number of links in contention range of a mesh node and the number of routes using each link. We show that our gateway placement algorithms outperform a greedy heuristic by up to 64 % on realistic topologies. For an example topology, we study the set of all possible gateway placements and find that there is large capacity gain between nearoptimal and optimal placements, but the nearoptimal placements found by local search are similar in configuration to the optimal. I.
Facility Location with Hierarchical Facility Costs
, 2006
"... We consider the facility location problem with hierarchical facility costs, and give a (4.236 + ffl)approximation algorithm using local search. The hierarchical facility location problem models multilevel service installation costs. Shmoys, Swamy and Levi [13] gave an approximation algorithm for a ..."
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Cited by 7 (1 self)
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We consider the facility location problem with hierarchical facility costs, and give a (4.236 + ffl)approximation algorithm using local search. The hierarchical facility location problem models multilevel service installation costs. Shmoys, Swamy and Levi [13] gave an approximation algorithm for a twolevel version of the problem.Here we consider a multilevel problem, and give a constant factor approximation algorithm, independent ofthe number of levels, for the case of identical costs on all facilities.
Distributed Server Migration for Scalable Internet Service Deployment
 SUBMITTED TO IEEE/ACM TRANSACTIONS ON NETWORKING MAY/XX/2008
, 2008
"... The effectiveness of service provisioning in largescale networks is highly dependent on the number and location of service facilities deployed at various hosts. The classical, centralized approach to determining the latter would amount to formulating and solving the uncapacitated kmedian (UKM) pro ..."
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Cited by 6 (4 self)
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The effectiveness of service provisioning in largescale networks is highly dependent on the number and location of service facilities deployed at various hosts. The classical, centralized approach to determining the latter would amount to formulating and solving the uncapacitated kmedian (UKM) problem (if the requested number of facilities is fixed), or the uncapacitated facility location (UFL) problem (if the number of facilities is also to be optimized). Clearly, such centralized approaches require knowledge of global topological and demand information, and thus do not scale and are not practical for large networks. The key question posed and answered in this paper is the following: “How can we determine in a distributed and scalable manner the number and location of service facilities?” We propose an innovative approach in which topology and demand information is limited to neighborhoods, or balls of small radius around selected facilities, whereas demand information is captured implicitly for the remaining (remote) clients outside these neighborhoods, by mapping them to clients on the edge of the neighborhood; the ball radius regulates the tradeoff between scalability and performance. We develop a scalable, distributed approach that answers our key question through an iterative reoptimization of the location and the number of facilities within such balls. We show that even for small values of the radius (1 or 2), our distributed approach achieves performance under various synthetic and real Internet topologies and workloads that is comparable to that of optimal, centralized approaches requiring full topology and demand information.