Prediction of Parallel Speed-ups for Las Vegas Algorithms

TL;DR

This paper introduces a probabilistic model to predict the parallel speed-ups of Las Vegas algorithms, demonstrating high accuracy in practical scenarios up to 256 cores by analyzing runtime distributions.

Contribution

The paper presents a novel probabilistic model for predicting parallel speed-ups of Las Vegas algorithms based on runtime distributions, validated through empirical experiments.

Findings

Prediction matches actual speedups up to 100 cores

Deviation of about 20% at 256 cores

Model effectively captures runtime variability

Abstract

We propose a probabilistic model for the parallel execution of Las Vegas algorithms, i.e., randomized algorithms whose runtime might vary from one execution to another, even with the same input. This model aims at predicting the parallel performances (i.e., speedups) by analysis the runtime distribution of the sequential runs of the algorithm. Then, we study in practice the case of a particular Las Vegas algorithm for combinatorial optimization, on three classical problems, and compare with an actual parallel implementation up to 256 cores. We show that the prediction can be quite accurate, matching the actual speedups very well up to 100 parallel cores and then with a deviation of about 20% up to 256 cores.