Jeanne Ferrante

Scheduling strategies for master-slave tasking on heterogeneous processor platforms

We consider the problem of allocating a large number of independent, equal-sized tasks to a heterogeneous computing platform. We use a nonoriented graph to model the platform, where resources can have different speeds of computation and communication. Because the number of tasks is large, we focus on the question of determining the optimal steady state scheduling strategy for each processor (the fraction of time spent computing and the fraction of time spent communicating with each neighbor). In contrast to minimizing the total execution time, which is NP-hard in most formulations, we show that finding the optimal steady state can be solved using a linear programming approach and, thus, in polynomial time. Our result holds for a quite general framework, allowing for cycles and multiple paths in the interconnection graph, and allowing for several masters. We also consider the simpler case where the platform is a tree. While this case can also be solved via linear programming, we show how to derive a closed-form formula to compute the optimal steady state, which gives rise to a bandwidth-centric scheduling strategy. The advantage of this approach is that it can directly support autonomous task scheduling based only on information local to each node; no global information is needed. Finally, we provide a theoretical comparison of the computing power of tree-based versus arbitrary platforms.

On Estimating and Enhancing Cache Effectiveness

In this paper, we consider automatic analysis of a programs cache usage to achieve greater cache effectiveness. We show how to estimate efficiently the number of distinct cache lines used by a given loop in a nest of loops. Given this estimate of the number of cache lines needed, we can estimate the number of cache misses for a nest of loops. Our estimates can be used to guide program transformations such as loop interchange to achieve greater cache effectiveness. We present simulation results that show our estimates are reasonable for simple cases such as matrix multiply. We analyze the array sizes for which our estimates differ from our simulation results, and provide recommendations on how to handle such arrays in practice.

A Decision Procedure for the First Order Theory of Real Addition with Order

Consider the first order theory of the real numbers with the function + (plus) and the predicate

Bandwidth-centric allocation of independent tasks on heterogeneous platforms

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Compile-time composition of run-time data and iteration reorderings

(less than). Let S be the set of true sentences of this theory. We first present an elimination of quantifiers decision procedure for S, and then analyze it to show that it takes at most time

Localizing non-affine array references

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Quantifying the multi-level nature of tiling interactions

, where c is a constant, to decide sentences of length n.We next show that a given sentence does not change in truth value when each of the quantifiers is limited to range over an appropriately chosen finite set of rationals. This fact leads to a new decision procedure for S which uses at most space

Schedule-independent storage mapping for loops

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Sparse Tiling for Stationary Iterative Methods

. We also remark that our methods lead to a decision procedure for Presburger arithmetic which operates within space

Selecting tile shape for minimal execution time

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