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90
Fast Approximation Algorithms for Fractional Packing and Covering Problems
, 1995
"... This paper presents fast algorithms that find approximate solutions for a general class of problems, which we call fractional packing and covering problems. The only previously known algorithms for solving these problems are based on general linear programming techniques. The techniques developed ..."
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Cited by 260 (13 self)
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This paper presents fast algorithms that find approximate solutions for a general class of problems, which we call fractional packing and covering problems. The only previously known algorithms for solving these problems are based on general linear programming techniques. The techniques developed in this paper greatly outperform the general methods in many applications, and are extensions of a method previously applied to find approximate solutions to multicommodity flow problems. Our algorithm is a Lagrangean relaxation technique; an important aspect of our results is that we obtain a theoretical analysis of the running time of a Lagrangean relaxationbased algorithm. We give several applications of our algorithms. The new approach yields several orders of magnitude of improvement over the best previously known running times for algorithms for the scheduling of unrelated parallel machines in both the preemptive and the nonpreemptive models, for the job shop problem, for th...
A Survey of Automated Timetabling
, 1999
"... The timetabling problem consists in scheduling a sequence of lectures between teachers and students in a prefixed period of time (typically a week), satisfying a set of constraints of various types. A large number of variants of the timetabling problem have been proposed in the literature, which d ..."
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Cited by 196 (16 self)
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The timetabling problem consists in scheduling a sequence of lectures between teachers and students in a prefixed period of time (typically a week), satisfying a set of constraints of various types. A large number of variants of the timetabling problem have been proposed in the literature, which differ from each other based on the type of institution involved (university or school) and the type of constraints. This problem, that has been traditionally considered in the operational research field, has recently been tackled with techniques belonging also to Artificial Intelligence (e.g., genetic algorithms, tabu search, and constraint satisfaction). In this paper, we survey the various formulations of the problem, and the techniques and algorithms used for its solution.
ChernoffHoeffding bounds for applications with limited independence.
 In Proceedings of the 4th Annual ACMSIAM Symposium on Discrete Algorithms,
, 1993
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Packet routing and jobshop scheduling in O(congestion+dilation) steps
 Combinatorica
, 1994
"... In this paper, we prove that there exists a schedule for routing any set of packets with edgesimple paths, on any network, in O(c+d) steps, where c is the congestion of the paths in the network, and d is the length of the longest path. The result has applications to packet routing in parallel machi ..."
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Cited by 119 (9 self)
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In this paper, we prove that there exists a schedule for routing any set of packets with edgesimple paths, on any network, in O(c+d) steps, where c is the congestion of the paths in the network, and d is the length of the longest path. The result has applications to packet routing in parallel machines, network emulations, and jobshop scheduling.
Deterministic JobShop Scheduling: Past, Present and Future
 European Journal of Operational Research
, 1998
"... : Due to the stubborn nature of the deterministic jobshop scheduling problem many solutions proposed are of hybrid construction cutting across the traditional disciplines. The problem has been investigated from a variety of perspectives resulting in several analytical techniques combining generic ..."
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Cited by 107 (2 self)
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: Due to the stubborn nature of the deterministic jobshop scheduling problem many solutions proposed are of hybrid construction cutting across the traditional disciplines. The problem has been investigated from a variety of perspectives resulting in several analytical techniques combining generic as well as problem specific strategies. We seek to assess a subclass of this problem in which the objective is minimising makespan, by providing an overview of the history, the techniques used and the researchers involved. The sense and direction of their work is evaluated by assessing the reported results of their techniques on the available benchmark problems. From these results the current situation and pointers for future work are provided. KEYWORDS: Scheduling Theory; JobShop; Review; Computational Study; 1. INTRODUCTION Current market trends such as consumer demand for variety, shorter product life cycles and competitive pressure to reduce costs have resulted in the need for zero i...
Improved scheduling algorithms for minsum criteria
 Automata, Languages and Programming, volume 1099 of Lecture Notes in Computer Science
, 1996
"... Abstract. We consider the problem of finding nearoptimal solutions for a variety of A/I)hard scheduling problems for which the objective is to minimize the total weighted completion time. Recent work has led to the development of several techniques that yield constant worstcase bounds in a number ..."
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Cited by 64 (18 self)
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Abstract. We consider the problem of finding nearoptimal solutions for a variety of A/I)hard scheduling problems for which the objective is to minimize the total weighted completion time. Recent work has led to the development of several techniques that yield constant worstcase bounds in a number of settings. We continue this line of research by providing improved performance guarantees for several of the most basic scheduling models, and by giving the first constant performance guarantee for a number of more realistically constrained scheduling problems. For example, we give an improved performance guarantee for minimizing the total weighted completion time subject to release dates on a single machine, and subject to release dates and/or precedence constraints on identical parallel machines. We also give improved bounds on the power of preemption in scheduling jobs with release dates on parallel machines. We give improved online algorithms for many more realistic scheduling models, including environments with parallelizable jobs, jobs contending for shared resources, tree precedenceconstrained jobs, as well as shop scheduling models. In several of these cases, we give the first constant performance guarantee achieved online. Finally, one of the consequences of our work is the surprising structural property that there are schedules that simultaneously approximate the optimal makespan and the optimal weighted completion time to within small constants. Not only do such schedules exist, but we can find approximations to them with an online algorithm. 1
Scheduling Split Intervals
, 2002
"... We consider the problem of scheduling jobs that are given as groups of nonintersecting segments on the real line. Each job Jj is associated with an interval, Ij, which consists of up to t segments, for some t _) 1, a of their segments intersect. Such jobs show up in a I.I Problem Statement and Mo ..."
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Cited by 63 (5 self)
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We consider the problem of scheduling jobs that are given as groups of nonintersecting segments on the real line. Each job Jj is associated with an interval, Ij, which consists of up to t segments, for some t _) 1, a of their segments intersect. Such jobs show up in a I.I Problem Statement and Motivation. We wide range of applications, including the transmission consider the problem of scheduling jobs that are given of continuousmedia data, allocation of linear resources as groups of nonintersecting segments on the real line. (e.g. bandwidth in linear processor arrays), and in Each job Jj is associated with a tinterval, Ij, which
Asymptotically optimal algorithm for job shop scheduling and packet routing
 J. Algorithms
, 1999
"... We propose asymptotically optimal algorithms for the job shop scheduling and packet routing problems. We propose a fluid relaxation for the job shop scheduling problem in which we replace discrete jobs with the flow of a continuous fluid. We compute an optimal solution of the fluid relaxation in clo ..."
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Cited by 59 (3 self)
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We propose asymptotically optimal algorithms for the job shop scheduling and packet routing problems. We propose a fluid relaxation for the job shop scheduling problem in which we replace discrete jobs with the flow of a continuous fluid. We compute an optimal solution of the fluid relaxation in closed form, obtain a lower bound Cmax to the job shop scheduling problem, and construct a feasible schedule from the fluid relaxation with objective value at most C � OŽ C. max ' max, where the constant in the OŽ. � notation is independent of the number of jobs, but it depends on the processing time of the jobs, thus producing an asymptotically optimal schedule as the total number of jobs tends to infinity. If the initially present jobs increase proportionally, then our algorithm produces a schedule with value at most C � OŽ. max 1. For the packet routing problem with fixed paths the previous algorithm applies directly. For the general packet routing problem we propose a linear programming relaxation that provides a lower bound Cmax and an asymptotically optimal algorithm that uses the optimal solution of the relaxation with objective value at most C � OŽ C. max ' max. Unlike asymptotically optimal algorithms that rely on probabilistic assumptions, our proposed algorithms make no probabilistic assumptions and they are asymptotically optimal for all instances with a large number of jobs Ž packets.. In computational experiments our algorithms produce schedules which are within 1 % of optimality even for moderately sized problems.
Job Shop Scheduling by Local Search
 INFORMS JOURNAL ON COMPUTING
, 1994
"... We survey solution methods for the job shop scheduling problem with an emphasis on local search. Both deterministic and randomized local search methods as well as the proposed neighborhoods are discussed. We compare the computational performance of the various methods in terms of their effectiveness ..."
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Cited by 55 (0 self)
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We survey solution methods for the job shop scheduling problem with an emphasis on local search. Both deterministic and randomized local search methods as well as the proposed neighborhoods are discussed. We compare the computational performance of the various methods in terms of their effectiveness and efficiency on a standard set of problem instances.
Minimizing Average Completion Time in the Presence of Release Dates
, 1995
"... A natural and basic problem in scheduling theory is to provide good average quality of service to a stream of jobs that arrive over time. In this paper we consider the problem of scheduling n jobs that are released over time in order to minimize the average completion time of the set of jobs. In con ..."
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Cited by 53 (8 self)
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A natural and basic problem in scheduling theory is to provide good average quality of service to a stream of jobs that arrive over time. In this paper we consider the problem of scheduling n jobs that are released over time in order to minimize the average completion time of the set of jobs. In contrast to the problem of minimizing average completion time when all jobs are available at time 0, all the problems that we consider are NPhard, and essentially nothing was known about constructing good approximations in polynomial time. We give the first constantfactor approximation algorithms for several variants of the single and parallel machine model. Many of the algorithms are based on interesting algorithmic and structural relationships between preemptive and nonpreemptive schedules and linear programming relaxations of both. Many of the algorithms generalize to the minimization of average weighted completion time as well. 1 Introduction Two important characteristics of many realw...