The Buuer Minimization Problem for Multiprocessor Scheduling with Connicts Icalp 2001 -submission for Track A

We consider the problem of scheduling a sequence of tasks in a multi-processor system with connicts. The term \connict" refers to a situation where two or more processors share common resources that can only be accessed by one processor at any given time. Connicting processors cannot process tasks at the same time. At certain times new tasks arrive in the system, where each task speciies the amount of work (processing time) added to each processor's workload. Each processor stores this workload in its input buuer. Our objective is to schedule task execution, obeying the connict constraints, and minimizing the maximum buuer size of all processors. In the oo-line case, we prove that, unless P = NP, the problem does not have a polynomial-time algorithm with a polynomial approximation ratio. In the on-line case, we provide the following results: (i) a competitive algorithm for general graphs, (ii) tight bounds on the competitive ratios for cliques and complete k-partite graphs, and (iii) a ((=2 + 1)-competitive algorithm for trees, where is the diameter. We also provide some additional results for small graphs with up to 4 vertices.