TEL-AVIV UNIVERSITY RAYMOND AND BEVERLY SACKLER FACULTY OF EXACT SCIENCES SCHOOL OF COMPUTER SCIENCE 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. One way in which this challenge was addressed is by statically partitioning the cache among the cores and assigning the jobs to the cores with the goal of minimizing the makespan. Several heuristic algorithms have been proposed that jointly decide how to partition the cache among the cores and how to assign the jobs. We initiate a theoretical study of this problem which we call the joint cache partition and job assignment problem. In this problem the input is a set of jobs, where each job is specified by a function that gives the running time of the job for each possible cache allocation. The goal is to statically partition a cache of size K among c cores and assign each job to a core such that the makespan is minimized. By a careful analysis of the space of possible cache partitions we obtain a constant approximation algorithm for this problem. We give better approximation algorithms for a few important special cases. We also provide lower and upper bounds on the improvement that can be obtained by allowing dynamic cache partitions and dynamic job assignments. We show that our joint cache partition and job assignment problem generalizes an interesting special case of the problem of scheduling on unrelated machines that is still more general than scheduling on related machines. In this special case the machines are ordered by their ”strength” and the running time of each job decreases when it is scheduled on a stronger machine. We call this problem the ordered unrelated machines scheduling problem. We give a polynomial time algorithm for scheduling on ordered unrelated machines for instances where each job has only two possible load values and the sets of load values for all jobs are of constant size.