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367
Primaldual approximation algorithms for metric facility location and kmedian problems
 Journal of the ACM
, 1999
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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 218 (31 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.
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 206 (5 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...
Nearoptimal network design with selfish agents
 IN PROCEEDINGS OF THE 35TH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING (STOC
, 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 124 (21 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 algorithm to find a (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 124 (7 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 100 (8 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.
BuyatBulk Network Design
"... Theessenceofthesimplestbuyatbulknetwork designproblemisbuyingnetworkcapacity"wholesale"toguaranteeconnectivityfromallnetwork nodestoacertaincentralnetworkswitch.Capacityissoldwith"volumediscount":themorecapacityisbought,thecheaperisthepriceperunit ofbandwidth.WeprovideO(log2n)r ..."
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Cited by 98 (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.
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 90 (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.
An Improved Approximation Ratio for the Minimum Latency Problem
 Mathematical Programming
, 1996
"... Given a tour visiting n points in a metric space, the latency of one of these points p is the distance traveled in the tour before reaching p. The minimum latency problem asks for a tour passing through n given points for which the total latency of the n points is minimum; in effect, we are seekin ..."
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Cited by 86 (2 self)
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Given a tour visiting n points in a metric space, the latency of one of these points p is the distance traveled in the tour before reaching p. The minimum latency problem asks for a tour passing through n given points for which the total latency of the n points is minimum; in effect, we are seeking the tour with minimum average "arrival time." This problem has been studied in the operations research literature, where it has also been termed the "deliveryman problem" and the "traveling repairman problem." The approximability of the minimum latency problem was first considered by Sahni and Gonzalez in 1976; however, unlike the classical traveling salesman problem, it is not easy to give any constantfactor approximation algorithm for the minimum latency problem. Recently, Blum, Chalasani, Coppersmith, Pulleyblank, Raghavan, and Sudan gave the first such algorithm, obtaining an approximation ratio of 144. In this work, we present an algorithm which improves this ratio to 21:55. The dev...
A primaldual approximation algorithm for generalized Steiner network problems
 Combinatorica
, 1995
"... M.I.T. We present the first polynomialtime 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, also called the survivable network design problem. ..."
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Cited by 84 (18 self)
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M.I.T. We present the first polynomialtime 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, also called the survivable network design problem. If k is the maximum cut requirement of the problem, our solution comes within a factor of 2k of optimal. Our algorithm is primaldual and shows the importance of this technique in designing approximation algorithms. 1