Makespan-Optimal Cache Partitioning

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In current multicore systems, cache memory is shared between multiple concurrent threads. Allocating the proper amount of cache to each thread is crucial to achieving high performance. Cache management in many existing systems is based on the least recently used replacement policy, which can lead to adverse contention between threads for shared cache space. Cache partitioning is a technique that reserves a certain amount of cache for each thread, and has been shown to work well in practice. We introduce the problem of determining the optimal cache partitioning to minimize the make span for completing a set of tasks. We analyze the problem using a model that generalizes a widely used empirical model for cache miss rates. Our first contribution is to give a mathematical characterization of the properties satisfied by an optimal partitioning. Second, we present an algorithm that finds a 1 +\epsilon approximation to the optimal partitioning in O(n log \frac{n}{\epsilon}log\frac{n}{\epsilon p}) time, where n is the number of tasks and p is a value that depends on the optimal solution. We compare our algorithm with several partitioning schemes used in practice or proposed in the literature. Simulations show that our algorithm achieves between 22-59% better make span compared to these algorithms.