Andreas S. Schulz

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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)
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)
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 maximizing a nondecreasing submodular set function over various constraint structures. Specifically, we explore the performance of the greedy algorithm, and a related variant, the locally greedy algorithm in solving submodular function maximization problems. Most classic results on the greedy algorithm and its variant assume the(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 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 completiontime formulation. We show their equivalence by proving that a O(n logn) greedy algorithm(More)
including environments with parallelizable jobs, jobs contending for shared resources, tree precedence-constrained jobs, as well as shop scheduling models. In several of these cases, we give the first constant performance guarantee achieved on-line. Finally, one of the consequences of our work is the surprising structural property that there are schedules(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)