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35
Cooperative Facility Location Games
 Journal of Algorithms
, 2000
"... The location of facilities in order to provide service for customers is a wellstudied problem in the operations research literature. In the basic model, there is a predefined cost for opening a facility and also for connecting a customer to a facility, the goal being to minimize the total cost. O ..."
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Cited by 57 (1 self)
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The location of facilities in order to provide service for customers is a wellstudied problem in the operations research literature. In the basic model, there is a predefined cost for opening a facility and also for connecting a customer to a facility, the goal being to minimize the total cost. Often, both in the case of public facilities (such as libraries, municipal swimming pools, fire stations, ...) and private facilities (such as distribution centers, switching stations, ...), we may want to find a `fair' allocation of the total cost to the customers  this is known as the cost allocation problem. A central question in cooperative game theory is whether the total cost can be allocated to the customers such that no coalition of customers has any incentive to build their own facility or to ask a competitor to service them.
Convex Quadratic and Semidefinite Programming Relaxations in Scheduling
 Journal of the ACM
, 1999
"... We consider the problem of scheduling unrelated parallel machines subject to release dates so as to minimize the total weighted completion time of jobs. The main contribution of this paper is a provably good convex quadratic programming relaxation of strongly polynomial size for this problem. The be ..."
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Cited by 33 (3 self)
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We consider the problem of scheduling unrelated parallel machines subject to release dates so as to minimize the total weighted completion time of jobs. The main contribution of this paper is a provably good convex quadratic programming relaxation of strongly polynomial size for this problem. The best previously known approximation algorithms are based on LP relaxations in time or intervalindexed variables. Those LP relaxations, however, suffer from a huge number of variables. As a result of the convex quadratic programming approach we can give a very simple and easy to analyze randomized 2approximation algorithm which can be further improved to performance guarantee 3#2 in the absence of release dates. We also consider preemptive scheduling problems and derive approximation algorithms and results on the power of preemption which improve upon the best previously known results for these settings. Finally, for the special case of two machines we introduce a more sophisticated semidefinite programming relaxation and apply the random hyperplane technique introduced by Goemans and Williamson for the MAXCUT problem
Semidefinite Relaxations, Multivariate Normal Distributions, and Order Statistics
, 1997
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APPROXIMATION ALGORITHMS FOR THE DISCRETE TIMECOST TRADEOFF PROBLEM
, 1998
"... Due to its obvious practical relevance, the TimeCost Tradeoff Problem has attracted the attention of many researchers over the last forty years. While the Linear TimeCost Tradeoff Problem can be solved in polynomial time, its discrete variant is known to be NPhard. We present the first approximat ..."
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Cited by 26 (0 self)
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Due to its obvious practical relevance, the TimeCost Tradeoff Problem has attracted the attention of many researchers over the last forty years. While the Linear TimeCost Tradeoff Problem can be solved in polynomial time, its discrete variant is known to be NPhard. We present the first approximation algorithms for the Discrete TimeCost Tradeoff Problem. Specifically, given a fixed budget we consider the problem of finding a shortest schedule for a project. We give an approximation algorithm with performance ratio 3/2 for the class of projects where all feasible durations of activities are either 0, 1, or 2. We extend our result by giving approximation algorithms with performance guarantee O(log l), where l is the ratio of the maximum duration of any activity to the minimum nonzero duration of any activity. Finally, we discuss bicriteria approximation algorithms which compute schedules for a given deadline or budget such that both project duration and cost are within a constant factor of the duration and cost of an optimum schedule for the given deadline or budget.
On Approximation Algorithms for the Minimum Satisfiability Problem
 Information Processing Letters
, 1996
"... this paper, our focus is on deterministic approximation algorithms for the MINSAT problem. From now on, we will use the word `heuristic' to mean a deterministic approximation algorithm which runs in polynomial time. Note that when the clauses are of size \Theta(n), where n is the number of vari ..."
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Cited by 24 (0 self)
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this paper, our focus is on deterministic approximation algorithms for the MINSAT problem. From now on, we will use the word `heuristic' to mean a deterministic approximation algorithm which runs in polynomial time. Note that when the clauses are of size \Theta(n), where n is the number of variables, the heuristic analyzed in [18] provides only a weak performance guarantee of \Theta(n). We present a simple approximationpreserving reduction from MINSAT to the minimum vertex cover (MINVC) problem. This reduction, in conjunction with known heuristics for the MINVC problem (see for example, [8,22]), yields a heuristic with a performance guarantee of 2 for MINSAT, thus improving the result of Kohli et al. [18]. We also show that MINSAT is as hard to approximate as MINVC; that is, if there is a heuristic with a performance guarantee ae for MINSAT, then there is a heuristic with the same performance guarantee ae for MINVC. Moreover, we show that this result holds even for MINSAT instances defined by Horn formulas. It has been conjectured in [12] that no polynomial approximation algorithm can provide a performance guarantee of 2 \Gamma ffl for any fixed ffl ? 0 for MINVC unless P = NP. Thus, our result provides an indication of the difficulty involved in devising a heuristic with a performance guarantee better than 2 for MINSAT.
Primaldual algorithms for deterministic inventory problems
 Math Oper Res
"... We consider several classical models in deterministic inventory theory: the singleitem lotsizing problem, the joint replenishment problem, and the multistage assembly problem. These inventory models have been studied extensively, and play a fundamental role in broader planning issues, such as th ..."
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Cited by 18 (5 self)
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We consider several classical models in deterministic inventory theory: the singleitem lotsizing problem, the joint replenishment problem, and the multistage assembly problem. These inventory models have been studied extensively, and play a fundamental role in broader planning issues, such as the management of supply chains. For each of these problems, we wish to balance the cost of maintaining surplus inventory for future demand against the cost of replenishing inventory more frequently. For example, in the joint replenishment problem, demand for several commodities is specified over a discrete finite planning horizon, the cost of maintaining inventory is linear in the number of units held, but the cost incurred for ordering a commodity is independent of the size of the order; furthermore, there is an additional fixed cost incurred each time a nonempty subset of commodities is ordered. The goal is to find a policy that satisfies all demands on time and minimizes the overall holding and ordering cost. We shall give a novel primaldual framework for designing algorithms for these models that significantly improve known results in several ways: the performance guarantees for the quality of the solutions improve on or match previously known results; the performance guarantees hold under much more general assumptions about the structure of the costs, and the algorithms and their analysis are significantly
Preemptive scheduling with rejection
, 2003
"... We consider the problem of preemptively scheduling a set of n jobs on m (identical, uniformly related, or unrelated) parallel machines. The scheduler may reject a subset of the jobs and thereby incur jobdependent penalties for each rejected job, and he must construct a schedule for the remaining jo ..."
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Cited by 17 (3 self)
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We consider the problem of preemptively scheduling a set of n jobs on m (identical, uniformly related, or unrelated) parallel machines. The scheduler may reject a subset of the jobs and thereby incur jobdependent penalties for each rejected job, and he must construct a schedule for the remaining jobs so as to optimize the preemptive makespan on the m machines plus the sum of the penalties of the jobs rejected. We provide a complete classification of these scheduling problems with respect to complexity and approximability. Our main results are on the variant with an arbitrary number of unrelated machines. This variant is APXhard, and we design a 1.58approximation algorithm for it. All other considered variants are weakly NPhard, and we provide fully polynomial time approximation schemes for them. Finally, we argue that our results for unrelated machines can be carried over to the corresponding preemptive open shop scheduling problem with rejection.
Semidefinite Relaxations for Parallel Machine Scheduling
 IN PROCEEDINGS OF THE 39TH ANNUAL IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS'98
, 1998
"... We consider the problem of scheduling unrelated parallel machines so as to minimize the total weighted completion time of jobs. Whereas the best previously known approximation algorithms for this problem are based on LP relaxations, we give a 3/2approximation algorithm that relies on a convex quadr ..."
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Cited by 15 (3 self)
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We consider the problem of scheduling unrelated parallel machines so as to minimize the total weighted completion time of jobs. Whereas the best previously known approximation algorithms for this problem are based on LP relaxations, we give a 3/2approximation algorithm that relies on a convex quadratic programming relaxation. For the special case of two machines we present a further improvement to a 1.2752approximation; we introduce a more sophisticated semidefinite programming relaxation and apply the random hyperplane technique introduced by Goemans and Williamson for the MAXCUT problem and its refined version of Feige and Goemans. To the best of our knowledge, this is the first time that convex and semidefinite programming techniques (apart from LPs) are used in the area of scheduling.
A Constant Approximation Algorithm for the OneWarehouse MultiRetailer Problem
 SUBMITTED TO MANAGEMENT SCIENCE
"... Deterministic inventory theory provides streamlined optimization models that attempt to capture tradeoffs in managing the flow of goods through a supply chain. We will consider two wellstudied deterministic inventory models, called the onewarehouse multiretailer problem (OWMR) and its special cas ..."
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Cited by 13 (3 self)
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Deterministic inventory theory provides streamlined optimization models that attempt to capture tradeoffs in managing the flow of goods through a supply chain. We will consider two wellstudied deterministic inventory models, called the onewarehouse multiretailer problem (OWMR) and its special case the joint replenishment problem (JRP), and give approximation algorithms with worstcase performance guarantees. That is, for each instance of the problem, our algorithm produces a solution with cost that is guaranteed to be at most 1.8 times the optimal cost; this is called a 1.8approximation algorithm. Our results are based on an LProunding approach; we provide the first constant approximation algorithm for the OWMR problem and improve the previous results for the JRP problem.
Rounding to an integral program
 In Proceedings of the 4th International Workshop on Efficient and Experimental Algorithms (WEA’05
, 2005
"... Abstract. We present a general framework for approximating several NPhard problems that have two underlying properties in common. First, the problems we consider can be formulated as integer covering programs, possibly with additional side constraints. Second, the number of covering options is rest ..."
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Cited by 11 (0 self)
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Abstract. We present a general framework for approximating several NPhard problems that have two underlying properties in common. First, the problems we consider can be formulated as integer covering programs, possibly with additional side constraints. Second, the number of covering options is restricted in some sense, although this property may be well hidden. Our method is a natural extension of the threshold rounding technique. 1