José Verschae

Dual techniques for scheduling on a machine with varying speed

We study scheduling problems on a machine of varying speed. Assuming a known speed function (given through an oracle) we ask for a cost-efficient scheduling solution. Our main result is a PTAS for minimizing the total weighted completion time on a machine of varying speed. This implies also a PTAS for the closely related problem of scheduling to minimize generalized global cost functions. The key to our results is a re-interpretation of the problem within the well-known two-dimensional Gantt chart: instead of the standard approach of scheduling in the time-dimension, we construct scheduling solutions in the weight-dimension. We also consider a dynamic problem variant in which deciding upon the speed is part of the scheduling problem and we are interested in the tradeoff between scheduling cost and speed-scaling cost, which is typically the energy consumption. We obtain two insightful results: (1) the optimal scheduling order is independent of the energy consumption and (2) the problem can be reduced to the setting where the speed of the machine is fixed, and thus admits a PTAS.

Scheduling periodic tasks in a hard real-time environment

We consider a real-time scheduling problem that occurs in the design of software-based aircraft control. The goal is to distribute tasks

Solving an avionics real-time scheduling problem by advanced IP-methods

au_i=(c_i,p_i)

The power of recourse for online MST and TSP

on a minimum number of identical machines and to compute offsets

A robust PTAS for machine covering and packing

a_i

The Power of Recourse for Online MST and TSP

for the tasks such that no collision occurs. A task

Closing the Gap for Makespan Scheduling via Sparsification Techniques

au_i

On the configuration-LP for scheduling on unrelated machines

releases a job of running time

How to Pack Your Items When You Have to Buy Your Knapsack

c_i

Strong LP formulations for scheduling splittable jobs on unrelated machines

at each time