Fast divide-and-conquer algorithms for preemptive scheduling problems with controllable processing times – A polymatroid optimization approach

We consider a variety of preemptive scheduling problems with controllable processing times on a single machine and on identical/uniform parallel machines, where the objective is to minimize the total compression cost. In this paper, we propose fast divide-and-conquer algorithms for these scheduling problems. Our approach is based on the observation that each scheduling problem we discuss can be formulated as a polymatroid optimization problem. We develop a novel divide-and-conquer technique for the polymatroid optimization problem and then apply it to each scheduling problem. We show that each scheduling problem can be solved in O(Tfeas(n) log n) time by using our divide-and-conquer technique, where n is the number of jobs and Tfeas(n) denotes the time complexity of the corresponding feasible scheduling problem with n jobs. This approach yields faster algorithms for most of the scheduling problems discussed in this paper

Decomposition algorithms for submodular optimization with applications to parallel machine scheduling with controllable processing times

In this paper we present a decomposition algorithm for maximizing a linear function over a submodular polyhedron intersected with a box. Apart from this contribution to submodular optimization, our results extend the toolkit available in deterministic machine scheduling with controllable processing times. We demonstrate how this method can be applied to developing fast algorithms for minimizing total compression cost for preemptive schedules on parallel machines with respect to given release dates and a common deadline. Obtained scheduling algorithms are faster and easier to justify than those previously known in the scheduling literature

Application of submodular optimization to single machine scheduling with controllable processing times subject to release dates and deadlines

In this paper, we study a scheduling problem on a single machine, provided that the jobs have individual release dates and deadlines, and the processing times are controllable. The objective is to find a feasible schedule that minimizes the total cost of reducing the processing times. We reformulate the problem in terms of maximizing a linear function over a submodular polyhedron intersected with a box. For the latter problem of submodular optimization, we develop a recursive decomposition algorithm and apply it to solving the single machine scheduling problem to achieve the best possible running time

Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization

International audienceThe Cologne-Twente Workshop (CTW) on Graphs and Combinatorial Optimization started off as a series of workshops organized bi-annually by either Köln University or Twente University. As its importance grew over time, it re-centered its geographical focus by including northern Italy (CTW04 in Menaggio, on the lake Como and CTW08 in Gargnano, on the Garda lake). This year, CTW (in its eighth edition) will be staged in France for the first time: more precisely in the heart of Paris, at the Conservatoire National d’Arts et Métiers (CNAM), between 2nd and 4th June 2009, by a mixed organizing committee with members from LIX, Ecole Polytechnique and CEDRIC, CNAM

LIPIcs, Volume 244, ESA 2022, Complete Volume

LIPIcs, Volume 244, ESA 2022, Complete Volum