This work presents the first known polynomial time approximation schemes for several variants of the problem of scheduling n jobs with release dates on m machines so as to minimize their average weighted completion time.Expand

A subtle variant of randomized rounding is introduced and new proofs for the existence of fair cost allocations for several classes of instances are derived, showing that it is in general NP-complete to decide whether a fair cost allocation exists and whether a given allocation is fair.Expand

Two simple randomized approximation algorithms are described, which are guaranteed to deliver feasible schedules with expected objective function value within factors of 1.7451 and 1.6853, respectively, of the optimum of two linear programming relaxations of the problem.Expand

This chapter gives an introduction into the fascinating area of flows over time—also called “dynamic flows” in the literature—and covers many exciting results that have been obtained over the last fifty years.Expand

It is proved that the first known results on the price of anarchy for flows over time can be seen as a concatenation of special static flows in the so-called deterministic queuing model that is very popular in road traffic simulation and related fields.Expand

We present a new class of randomized approximation algorithms for unrelated parallel machine scheduling problems with the average weighted completion time objective. The key idea is to assign jobs… Expand

A provably good convex quadratic programming relaxation of strongly polynomial size is proposed for this problem of scheduling unrelated parallel machines subject to release dates so as to minimize the total weighted completion time of jobs.Expand

A procedure for controlling a data processing system by a computer program that compares two versions of a source program and identifies the difference between the two. The program compares the two… Expand

The first approximation algorithms for the Discrete Time-Cost Tradeoff Problem are presented, which consider the problem of finding a shortest schedule for a project and 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.Expand

It is proved that the complexity of (fractional) 'multicommodity flows over time' is NP-hard, even for series-parallel networks, and new and efficient algorithms under certain assumptions on the transit times or on the network topology are presented.Expand