Processor Allocation for Optimistic Parallelization of Irregular Programs

TL;DR

This paper introduces a systematic approach for processor allocation in optimistic parallelization of irregular algorithms, utilizing conflict graphs and theoretical bounds to optimize resource distribution amid dynamic parallelism.

Contribution

It presents the first comprehensive strategy for processor allocation in irregular algorithms, leveraging conflict graphs and theoretical bounds to improve parallelism management.

Findings

Conflict graph analysis provides insight into parallelism potential.

Extended Turán's theorem offers a lower bound on exploitable parallelism.

Heuristic control strategy is effective and stable in experiments.

Abstract

Optimistic parallelization is a promising approach for the parallelization of irregular algorithms: potentially interfering tasks are launched dynamically, and the runtime system detects conflicts between concurrent activities, aborting and rolling back conflicting tasks. However, parallelism in irregular algorithms is very complex. In a regular algorithm like dense matrix multiplication, the amount of parallelism can usually be expressed as a function of the problem size, so it is reasonably straightforward to determine how many processors should be allocated to execute a regular algorithm of a certain size (this is called the processor allocation problem). In contrast, parallelism in irregular algorithms can be a function of input parameters, and the amount of parallelism can vary dramatically during the execution of the irregular algorithm. Therefore, the processor allocation problem for irregular algorithms is very difficult. In this paper, we describe the first systematic strategy for addressing this problem. Our approach is based on a construct called the conflict graph, which (i) provides insight into the amount of parallelism that can be extracted from an irregular algorithm, and (ii) can be used to address the processor allocation problem for irregular algorithms. We show that this problem is related to a generalization of the unfriendly seating problem and, by extending Tur\'an's theorem, we obtain a worst-case class of problems for optimistic parallelization, which we use to derive a lower bound on the exploitable parallelism. Finally, using some theoretically derived properties and some experimental facts, we design a quick and stable control strategy for solving the processor allocation problem heuristically.