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415
Approximation algorithms for metric facility location and kmedian problems using the . . .
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A Factor 2 Approximation Algorithm for the Generalized Steiner Network Problem
 Combinatorica
"... We present a factor 2 approximation algorithm for finding a minimumcost subgraph having at least a specified number of edges in each cut. This class of problems includes, among others, the generalized Steiner network problem, which is also known as the survivable network design problem. Our algorit ..."
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Cited by 270 (3 self)
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We present a factor 2 approximation algorithm for finding a minimumcost subgraph having at least a specified number of edges in each cut. This class of problems includes, among others, the generalized Steiner network problem, which is also known as the survivable network design problem. Our algorithm first solves the linear relaxation of this problem, and then iteratively rounds off the solution. The key idea in rounding off is that in a basic solution of the LP relaxation, at least one edge gets included at least to the extent of half. We include this edge into our integral solution and solve the residual problem. 1 Introduction We consider the problem of finding a minimumcost subgraph of a given graph such that the number of edges crossing each cut is at least a specified requirement. Formally, given an undirected multigraph G = (V; E), a nonnegative cost function c : E ! Q+ , and a requirement function f : 2 V ! Z , solve the following integer program (IP): min X e2E c e x...
When trees collide: An approximation algorithm for the generalized Steiner problem on networks
, 1994
"... We give the first approximation algorithm for the generalized network Steiner problem, a problem in network design. An instance consists of a network with linkcosts and, for each pair fi; jg of nodes, an edgeconnectivity requirement r ij . The goal is to find a minimumcost network using the a ..."
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Cited by 256 (39 self)
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We give the first approximation algorithm for the generalized network Steiner problem, a problem in network design. An instance consists of a network with linkcosts and, for each pair fi; jg of nodes, an edgeconnectivity requirement r ij . The goal is to find a minimumcost network using the available links and satisfying the requirements. Our algorithm outputs a solution whose cost is within 2dlog 2 (r + 1)e of optimal, where r is the highest requirement value. In the course of proving the performance guarantee, we prove a combinatorial minmax approximate equality relating minimumcost networks to maximum packings of certain kinds of cuts. As a consequence of the proof of this theorem, we obtain an approximation algorithm for optimally packing these cuts; we show that this algorithm has application to estimating the reliability of a probabilistic network.
Nearoptimal network design with selfish agents
, 2003
"... We introduce a simple network design game that models how independent selfish agents can build or maintain a large network. In our game every agent has a specific connectivity requirement, i.e. each agent has a set of terminals and wants to build a network in which his terminals are connected. Possi ..."
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Cited by 156 (19 self)
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We introduce a simple network design game that models how independent selfish agents can build or maintain a large network. In our game every agent has a specific connectivity requirement, i.e. each agent has a set of terminals and wants to build a network in which his terminals are connected. Possible edges in the network have costs and each agent’s goal is to pay as little as possible. Determining whether or not a Nash equilibrium exists in this game is NPcomplete. However, when the goal of each player is to connect a terminal to a common source, we prove that there is a Nash equilibrium as cheap as the optimal network, and give a polynomial time algorithmtofinda(1+ε)approximate Nash equilibrium that does not cost much more. For the general connection game we prove that there is a 3approximate Nash equilibrium that is as cheap as the optimal network, and give an algorithm to find a (4.65 +ε)approximate Nash equilibrium that does not cost much more.
THE PRIMALDUAL METHOD FOR APPROXIMATION ALGORITHMS AND ITS APPLICATION TO NETWORK DESIGN PROBLEMS
"... The primaldual method is a standard tool in the design of algorithms for combinatorial optimization problems. This chapter shows how the primaldual method can be modified to provide good approximation algorithms for a wide variety of NPhard problems. We concentrate on results from recent researc ..."
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Cited by 142 (5 self)
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The primaldual method is a standard tool in the design of algorithms for combinatorial optimization problems. This chapter shows how the primaldual method can be modified to provide good approximation algorithms for a wide variety of NPhard problems. We concentrate on results from recent research applying the primaldual method to problems in network design.
A nearly bestpossible approximation algorithm for nodeweighted Steiner trees
, 1993
"... We give the first approximation algorithm for the nodeweighted Steiner tree problem. Its performance guarantee is within a constant factor of the best possible unless ~ P ' NP . Our algorithm generalizes to handle other network design problems. ..."
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Cited by 138 (10 self)
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We give the first approximation algorithm for the nodeweighted Steiner tree problem. Its performance guarantee is within a constant factor of the best possible unless ~ P ' NP . Our algorithm generalizes to handle other network design problems.
The Prize Collecting Steiner Tree Problem
 In Proceedings of the 11th Annual ACMSIAM Symposium on Discrete Algorithms
, 1998
"... This work is motivated by an application in local access network design that can be modeled using the NPhard Prize Collecting Steiner Tree problem. We consider several variants on this problem and on the primaldual 2approximation algorithm devised for it by Goemans and Williamson. We develop seve ..."
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Cited by 103 (1 self)
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This work is motivated by an application in local access network design that can be modeled using the NPhard Prize Collecting Steiner Tree problem. We consider several variants on this problem and on the primaldual 2approximation algorithm devised for it by Goemans and Williamson. We develop several modifications to the algorithm which lead to theoretical as well as practical improvements in the performance of the algorithm for the original problem. We also demonstrate how already existing algorithms can be extended to solve the bicriteria variants of the problem with constant factor approximation guarantees. Our work leads to practical heuristics applicable in network design.
BuyatBulk Network Design
"... Theessenceofthesimplestbuyatbulknetwork designproblemisbuyingnetworkcapacity"wholesale"toguaranteeconnectivityfromallnetwork nodestoacertaincentralnetworkswitch.Capacityissoldwith"volumediscount":themorecapacityisbought,thecheaperisthepriceperunit ofbandwidth.WeprovideO(log2n)r ..."
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Cited by 103 (0 self)
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Theessenceofthesimplestbuyatbulknetwork designproblemisbuyingnetworkcapacity"wholesale"toguaranteeconnectivityfromallnetwork nodestoacertaincentralnetworkswitch.Capacityissoldwith"volumediscount":themorecapacityisbought,thecheaperisthepriceperunit ofbandwidth.WeprovideO(log2n)randomized approximationalgorithmfortheproblem.This solvestheopenproblemin[15].Theonlypreviouslyknownsolutionswererestrictedtospecial cases(Euclideangraphs)[15]. Wesolveadditionalnaturalvariationsofthe problem,suchasmultisinknetworkdesign,as wellasselectivenetworkdesign.Theseproblems canbeviewedasgeneralizationsofthetheGeneralizedSteinerConnectivityandPrizecollecting salesman(KMST)problems. Intheselectivenetworkdesignproblem,some subsetofkwellsmustbeconnectedtothe(single) renery,sothatthetotalcostisminimized.
Improved Approximation Algorithms for Network Design Problems
, 1994
"... We consider a class of network design problems in which one needs to find a minimumcost network satisfying certain connectivity requirements. For example, in the survivable network design problem, the requirements specify that there should be at least r(v; w) edgedisjoint paths between each pai ..."
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Cited by 102 (11 self)
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We consider a class of network design problems in which one needs to find a minimumcost network satisfying certain connectivity requirements. For example, in the survivable network design problem, the requirements specify that there should be at least r(v; w) edgedisjoint paths between each pair of vertices v and w. We present an approximation algorithm with a performance guarantee of 2H(fmax ) = 2(1 + 2 + 3 + \Delta \Delta \Delta + fmax ) where fmax is the maximum requirement. This improves upon the best previously known performance guarantee of 2fmax . We also show
Computing MinimumWeight Perfect Matchings
 INFORMS
, 1999
"... We make several observations on the implementation of Edmonds’ blossom algorithm for solving minimumweight perfectmatching problems and we present computational results for geometric problem instances ranging in size from 1,000 nodes up to 5,000,000 nodes. A key feature in our implementation is the ..."
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Cited by 102 (2 self)
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We make several observations on the implementation of Edmonds’ blossom algorithm for solving minimumweight perfectmatching problems and we present computational results for geometric problem instances ranging in size from 1,000 nodes up to 5,000,000 nodes. A key feature in our implementation is the use of multiple search trees with an individual dualchange � for each tree. As a benchmark of the algorithm’s performance, solving a 100,000node geometric instance on a 200 Mhz PentiumPro computer takes approximately 3 minutes.