Algorithms for scheduling with conflicts

Scheduling with conflicts supposes graph of conflicts. Vertices of that graph represent machines and edges represent conflicts between them. Every machine can be switched on or switched off . Two conflicting machines cannot be both switched on at the same time. At certain times new tasks arrive to speci c machines and enqueue to its input buff ers. Each machine continuously processes tasks from its input bu ffer whenever it is switched on. An algorithm decides which machines should be switched on or switched o ff at any time, obeying conflict constraints. The objective is to schedule machine switching to minimize the maximum bu er size of all processors. The problem is online, so an algorithm has to make decisions about current con ffiguration without knowledge of future tasks. In this thesis I consider the algorithm based on maximization of scalar product of work vector (vector describing con guration of machines) and vector of bu ffer lengths. I prove that this algorithm is well de ffined, finite on every input and for speciffi c graph (path of length 3) it has competitive ratio of 7=3. Further I consider possibilities of implementation of that algorithm