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39
Approximation Algorithms for Geometric Median Problems
, 1992
"... In this paper we present approximation algorithms for median problems in metric spaces and fixeddimensional Euclidean space. Our algorithms use a new method for transforming an optimal solution of the linear program relaxation of the smedian problem into a provably good integral solution. This ..."
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Cited by 70 (0 self)
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In this paper we present approximation algorithms for median problems in metric spaces and fixeddimensional Euclidean space. Our algorithms use a new method for transforming an optimal solution of the linear program relaxation of the smedian problem into a provably good integral solution. This transformation technique is fundamentally different from the methods of randomized and deterministic rounding [Rag, RaT] and the methods proposed in [LiV] in the following way: Previous techniques never set variables with zero values in the fractional solution to 1. This departure from previous methods is crucial for the success of our algorithms.
Rounding via Trees: Deterministic Approximation Algorithms for Group Steiner Trees and kmedian
 In Proceedings of the 30th Annual ACM Symposium on Theory of Computing
, 1998
"... Most optimization problems on an undirected graph reduce in complexity when restricted to instances on a tree. A recent result [3] for probabilistically approximating graph metrics by trees such that no edge stretches (in an expected sense) by more than a factor of O(log 2 n) has resulted in several ..."
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Cited by 56 (8 self)
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Most optimization problems on an undirected graph reduce in complexity when restricted to instances on a tree. A recent result [3] for probabilistically approximating graph metrics by trees such that no edge stretches (in an expected sense) by more than a factor of O(log 2 n) has resulted in several approximation algorithms which exploit the ease of solving problems on trees. The tree construction in [3] is inherently randomized and a natural question to ask is whether approximation algorithms which use this construction can be derandomized. We present a general framework for derandomizing approximation algorithms which use the above tree construction as a primitive. Let \Pi be a graph optimization problem which can be expressed as an integer program with 01 variables ¯ x(e) for each edge and with an objective function expressible as...
The Access Network Design Problem
 39th IEEE Symposium on Foundations of Computer Science
, 1998
"... We consider the problem of designing a minimum cost access network to carry traffic from a set of endnodes to a core network. A set of trunks of K differing types are available for leasing or buying. Some trunktypes have a high initial overhead cost but a low cost per unit bandwidth. Others have a ..."
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Cited by 47 (1 self)
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We consider the problem of designing a minimum cost access network to carry traffic from a set of endnodes to a core network. A set of trunks of K differing types are available for leasing or buying. Some trunktypes have a high initial overhead cost but a low cost per unit bandwidth. Others have a low overhead cost but a high cost per unit bandwidth. When the central core is given, we show how to construct an access network whose cost is within O(K 2 ) of optimal, under weak assumptions on the cost structure. In contrast with previous bounds, this bound is independent of the network and the traffic. Typically, the value of K is small. Our approach uses a linear programming relaxation and is motivated by a rounding technique of Shmoys, Tardos and Aardal [15]. Our techniques extend to a more complex situation in which the core is not given a priori. In this case we aim to minimize the switch cost of the core in addition to the trunk cost of the access network. We provide the same pe...
Approximation Algorithms for PrecedenceConstrained Scheduling Problems on Parallel Machines That Run At Different Speeds (Extended Abstracts)
"... We present new approximation algorithms for the problem of scheduling precedenceconstrained jobs on parallel machines that are uniformly related. That is, there are n jobs and m machines; each job j requires p j units of processing, and is to be processed on one machine without interruption; if it ..."
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Cited by 41 (1 self)
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We present new approximation algorithms for the problem of scheduling precedenceconstrained jobs on parallel machines that are uniformly related. That is, there are n jobs and m machines; each job j requires p j units of processing, and is to be processed on one machine without interruption; if it is assigned to machine i, which runs at a given speed s i , it takes p j =s i time units. There also is a partial order OE on the jobs, where j OE k implies that job k may not start processing until job j has been completed. We shall consider two objective functions: Cmax = max j C j , where C j denotes the completion time of job j, and P j w j C j , where w j is a weight that is given for each job j. For the first
The Constrained Minimum Spanning Tree Problem (Extended Abstract)
"... Given an undirected graph with two different nonnegative costs associated with every edge e (say, we for the weight and le for the length of edge e) and a budget L, consider the problem of finding a spanning tree of total edge length at most L and minimum total weight under this restriction. This co ..."
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Cited by 35 (3 self)
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Given an undirected graph with two different nonnegative costs associated with every edge e (say, we for the weight and le for the length of edge e) and a budget L, consider the problem of finding a spanning tree of total edge length at most L and minimum total weight under this restriction. This constrained minimum spanning tree problem is weakly NPhard. We present a polynomialtime approximation scheme for this problem. This algorithm always produces a spanning tree of total length at most (1 + e)L and of total weight at most that of any spanning tree of total length at most L, for any fixed e> 0. The algorithm uses Lagrangean relaxation, and exploits adjacency relations for matroids.
Computing NearOptimal Solutions to Combinatorial Optimization Problems
 IN COMBINATORIAL OPTIMIZATION, DIMACS SERIES IN DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
, 1995
"... In the past few years, there has been significant progress in our understanding of the extent to which nearoptimal solutions can be efficiently computed for NPhard combinatorial optimization problems. This paper surveys these recent developments, while concentrating on the advances made in the ..."
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Cited by 31 (0 self)
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In the past few years, there has been significant progress in our understanding of the extent to which nearoptimal solutions can be efficiently computed for NPhard combinatorial optimization problems. This paper surveys these recent developments, while concentrating on the advances made in the design and analysis of approximation algorithms, and in particular, on those results that rely on linear programming and its generalizations.
Approximation Algorithms for the Traveling Purchaser Problem and its Variants in Network Design
, 1999
"... . The traveling purchaser problem is a generalization of the traveling salesman problem with applications in a wide range of areas including network design and scheduling. The input consists of a set of markets and a set of products. Each market offers a price for each product and there is a cos ..."
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Cited by 26 (5 self)
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. The traveling purchaser problem is a generalization of the traveling salesman problem with applications in a wide range of areas including network design and scheduling. The input consists of a set of markets and a set of products. Each market offers a price for each product and there is a cost associated with traveling from one market to another. The problem is to purchase all products by visiting a subset of the markets in a tour such that the total travel and purchase costs are minimized. This problem includes many wellknown NPhard problems such as uncapacitated facility location, set cover and group Steiner tree problems as its special cases. We give an approximation algorithm with a polylogarithmic worstcase ratio for the traveling purchaser problem with metric travel costs. For a special case of the problem that models the ringstar network design problem, we give a constantfactor approximation algorithm. Our algorithms are based on rounding LP relaxation sol...
Dynamic and Static Algorithms for Optimal Placement of Resources in a Tree
 THEORETICAL COMPUTER SCIENCE
, 1996
"... We consider the problem of placing resources in trees. We give algorithms for the static and dynamic version of the problem. The static algorithms are faster than the algorithms found in literature, while the dynamic algorithms are the first for this problem and run in polylogarithmic time. ..."
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Cited by 15 (1 self)
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We consider the problem of placing resources in trees. We give algorithms for the static and dynamic version of the problem. The static algorithms are faster than the algorithms found in literature, while the dynamic algorithms are the first for this problem and run in polylogarithmic time.
Approximation Algorithms for Clustering Problems
, 2004
"... Clustering is a ubiquitous problem that arises in many applications in different fields such as data mining, image processing, machine learning, and bioinformatics. Clustering problems have been extensively studied as optimization problems with various objective functions in the Operations Research ..."
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Cited by 14 (5 self)
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Clustering is a ubiquitous problem that arises in many applications in different fields such as data mining, image processing, machine learning, and bioinformatics. Clustering problems have been extensively studied as optimization problems with various objective functions in the Operations Research and Computer Science literature. We focus on a class of objective functions more commonly referred to as facility location problems. These problems arise in a wide range of applications such as, plant or warehouse location problems, cache placement problems, and network design problems where the costs obey economies of scale. In the simplest of these problems, the uncapacitated facility location (UFL) problem, we want to open facilities at some subset of a given set of locations and assign each client in a given set D to an open facility so as to minimize the sum of the facility opening costs and client assignment costs. This is a very wellstudied problem; however it fails to address many of the requirements of real applications. In this thesis we consider various problems that build upon UFL and capture additional issues that arise in applications such as, uncertainties in the data, clients with different service needs, and facilities with interconnectivity requirements. By focusing initially on facility location problems in these new models, we develop new algorithmic techniques that will find application in a wide range of settings. We consider a widely used paradigm in stochastic programming to model settings where the underlying data, for example, the locations or demands of the clients, may be uncertain: the 2stage with recourse model that involves making some initial decisions, observing additional information, and then augmenting the initial decisions, if necessary, by taking recourse actions. We present a randomized polynomial time
Tight Approximations for Resource Constrained Scheduling and Bin Packing
 IN PROCEEDINGS OF THE SECOND EUROPEAN SYMPOSIUM ON ALGORITHMS
, 1994
"... We consider the following resource constrained scheduling problem. Given m identical processors, s resources with upper bounds, n independent tasks of unit length, where each task has a start time and requires one processor and a taskdependent amount of every resource. The optimization problem is t ..."
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Cited by 9 (1 self)
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We consider the following resource constrained scheduling problem. Given m identical processors, s resources with upper bounds, n independent tasks of unit length, where each task has a start time and requires one processor and a taskdependent amount of every resource. The optimization problem is to schedule all tasks at discrete times in IIN, minimizing the latest completion time Cmax subject to the processor, resource and starttime constraints. Multidimensional bin packing is a special case of this problem. The problem is NPhard even under much simpler assumptions. In case of zero start times Rock and Schmidt (1983) showed an (m=2)factor approximation algorithm and de la Vega and Lueker (1981), improving a classical result of Garey, Graham, Johnson and Yao (1976), gave for every ffl ? 0 a linear time algorithm with an asymptotic approximation guarantee of s + ffl. The contribution of this paper is to break the O(m) resp. O(s) barrier, even in the case of zero start times, at leas...