In the (non-preemptive) Generalized Min Sum Set Cover Problem, we are given n ground elements and a collection of sets S = {S1, S2, ..., Sm} where each set Si ∈ 2 has a positive requirement κ(Si) that has to be fulfilled. We would like to order all elements to minimize the total (weighted) cover time of all sets. The cover time of a set Si is defined as the first index j in the ordering such th...

Since its introduction in 1985, competitive analysis is a widely used tool for the performance measurement of online algorithms. Despite simplicity and popularity, has own set drawbacks which lead to development other measures. However, these measures were seldom applied problems domains. Recently Boyar et al . ( Theor. Comput. Sci 532 (2014) 2–13) studied search problem using various non-preem...

In this paper, the RCPSP (Resource Constrained Project Scheduling Problem) is solved using a linear programming model. Each activity may or may not be preemptive. Each variable is associated to a subset of independent activities (antichains). The properties of the model are first investigated. In particular, conditions are given that allow a solution of the linear program to be a feasible sched...

We study the classical problem of scheduling a set of independent jobs with release dates on a single machine. There exists a huge literature on the preemptive version of the problem, where the jobs can be interrupted at any moment. However, we focus here on the non-preemptive case, which is harder, but more relevant in practice. For instance, the jobs submitted to actual high performance platf...