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In this paper we introduce two general techniques for the design and analysis of approximation algorithms for NP-hard scheduling problems in which the objective is to minimize the weighted sum of the job completion times. For a variety of scheduling models, these techniques yield the rst algorithms that are guaranteed to nd schedules that have objective… (More)

According to Wardrop's first principle, agents in a congested network choose their routes selfishly, a behavior that is captured by the Nash equilibrium of the underlying noncooperative game. A Nash equilibrium does not optimize any global criterion per se, and so there is no apparent reason why it should be close to a solution of minimal total travel time,… (More)

There has been recent success in using polyhedral formulations of scheduling problems not only to obtain good lower bounds in practice but also to develop provably good approximation algorithms. Most of these formulations rely on binary decision variables that are a kind of assignment variables. We present quite simple polynomial-time approximation… (More)

We consider the problem of nding near-optimal solutions for a variety of NP-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 worst-case bounds in a number of settings. We continue this line of research by providing improved… (More)

In this paper, we provide a new class of randomized approximation algorithms for parallel machine scheduling problems. The most general model we consider is scheduling unrelated machines with release dates (or even network scheduling) so as to minimize the average weighted completion time. We introduce an LP relaxation in time-indexed variables for this… (More)

We consider the scheduling problem of minimizing the average weighted completion time of n jobs with release dates on a single machine. We first study two linear programming relaxations of the problem, one based on a time-indexed formulation, the other on a completion-time formulation. We show their equivalence by proving that a O(n log n) greedy algorithm… (More)

In machine scheduling, a set of n jobs must be scheduled on a set of m machines. Each job i incurs a processing time of pij on machine j and the goal is to schedule jobs so as to minimize some global objective function, such as the maximum makespan of the schedule considered in this paper. Often in practice, each job is controlled by an independent selfish… (More)

We discuss the problem of sequencing precedence-constrained jobs on a single machine to minimize the average weighted completion time. This problem has attracted much attention in the mathematical programming community since Sidney's pioneering work in 1975 (Sidney, J. B. 1975. Decomposition algorithms for single machine scheduling with precedence relations… (More)

We consider the problem to minimize the total weighted completion time of a set of jobs with individual release dates which have to be scheduled on identical parallel machines. Job processing times are not known in advance, they are realized on-line according to given probability distributions. The aim is to find a scheduling policy that minimizes the… (More)