Joint Cache Partition and Job Assignment on Multi-Core Processors

Multicore shared cache processors pose a challenge for designers of embedded systems who try to achieve minimal and predictable execution time of workloads consisting of several jobs. To address this challenge the cache is statically partitioned among the cores and the jobs are assigned to the cores so as to minimize the makespan. Several heuristic algorithms have been proposed that jointly decide how to partition the cache among the cores and assign the jobs. We initiate a theoretical study of this problem which we call the joint cache partition and job assignment problem. By a careful analysis of the possible cache partitions we obtain a constant approximation algorithm for this problem. For some practical special cases we obtain a 2-approximation algorithm, and show how to improve the approximation factor even further by allowing the algorithm to use additional cache. We also study possible improvements that can be obtained by allowing dynamic cache partitions and dynamic job assignments. We define a natural special case of the well known scheduling problem on unrelated machines in which machines are ordered by "strength". Our joint cache partition and job assignment problem generalizes this scheduling problem which we think is of independent interest. We give a polynomial time algorithm for this scheduling problem for instances obtained by fixing the cache partition in a practical case of the joint cache partition and job assignment problem where job loads are step functions

Complexity results for scheduling tasks in fixed intervals on two types of machines

Suppose that $n$ independent tasks are to be scheduled without preemption on an unlimited number of parallel machines of two types: inexpensive slow machines and expensive fast machines. Each task requires a given processing time on a slow machine or a given smaller processing time on a fast machine. We make two different feasibility assumptions: (a) each task has a specified processing interval, the length of which is equal to the processing time on a slow machine; (b) each task has a specified starting time. For either problem type, we wish to find a feasible schedule of minimum total machine cost. It is shown that both problems are NP-hard in the strong sense. These results are complemented by polynomial algorithms for some special cases