<abstract><p>We consider a basic preemptive scheduling problem where $ n non-simultaneously released jobs are to be processed by m unrelated parallel machines so as minimize maximum job completion time. An optimal LP-solution has been used construct an schedule for simultaneously in time O(n^3) $. We propose fast O(m) algorithm that finds case the above possesses "small enough" numb...

We provide several non-approximability results for deterministic scheduling problems whose objective is to minimize the total job completion time. Unless P = NP, none of the problems under consideration can be approximated in polynomial time within arbitrarily good precision. Most of our results are derived by APX-hardness proofs. We show that, whereas scheduling on unrelated machines with unit...

The paper investigates a stochastic production scheduling problem with unrelated parallel machines. A closed-loop scheduling technique is presented that on-line controls the production process. To achieve this, the scheduling problem is reformulated as a special Markov Decision Process. A near-optimal control policy of the resulted MDP is calculated in a homogeneous multi-agent system. Each age...

m unrelated parallel machines scheduling problems with variable job processing times are considered, where the processing time of a job is a function of its position in a sequence, its starting time, and its resource allocation. The objective is to determine the optimal resource allocation and the optimal schedule to minimize a total cost function that dependents on the total completion (waitin...

We combine the pipage rounding technique of Ageev & Sviridenko witha recent rounding method developed by Srinivasan, to develop a new randomized rounding approach for fractional vectors defined on the edge-sets of bipartite graphs. We show various ways of combining this technique with other ideas, leading to the following applications: richer random-graph models for graphs with a given degree-s...