Preemptive open shop scheduling can be viewed as an edge coloring problem in a bipartite multigraph. In some applications, restrictions of colors (in particular preassignments) are made for some edges. We give characterizations of graphs where some special preassignments can be embedded in a minimum coloring (number of colors = maximum degree). The case of restricted colorings of trees is shown...

We use the duality of linear programing to obtain exact formulas of competitive ratio for the semi-online preemptive scheduling on three and four machines. We use the linear programs from [5]. Namely we consider the online scheduling and the semi-online scheduling with known sum of processing times. We solve the linear programs symbolically by examining all basic solution candidates. All soluti...

We consider the problem of scheduling on parallel uniformly related machines, where preemptions are allowed and the machines are controlled by selfish agents. Our goal is to minimize the makespan, whereas the goal of the agents is to maximize their profit. We show that a known algorithm is monotone and can therefore be used to create a truthful mechanism for this problem which achieves the opti...

Discrete scheduling is preferred over continuous scheduling for preemptive scheduling problems, however, classical continuous schedulability tests can not work effectively with discrete scheduling. This area of integrating discrete scheduling with continuous schedulability tests remains unexplored. Two contributions are made in this paper; firstly, an empty-slot method is introduced and extende...

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...

The network of workstations (NOW) we consider for local scheduling of parallel tasks and communications is heterogeneous and nondedicated, where computing power varies among the workstations, and multiple jobs may interact with each other in execution. Local scheduling is a standard method on networks of workstations, where each node in the system makes independent scheduling decisions. Coordin...

A priority based packet scheduling scheme is proposed which aims at scheduling different types of data packets, such as real time and non-real-time data packets at sensor nodes with resource constraints in Wireless Sensor Networks. Most of the existing packet-scheduling mechanisms of Wireless Sensor Networks use First Come First Served (FCFS), non-preemptive priority and preemptive priority sch...