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 restriction of the well known scheduling problem on unrelated machines in which machines are ordered by "strength". We call this restriction the ordered unrelated machines scheduling problem. We show that our joint cache partition and job assignment problem is harder than this scheduling problem. The ordered unrelated machines scheduling problem is of independent interest and we give a polynomial time algorithm for certain natural workloads.