Parallel Galton Watson Process

TL;DR

This paper presents a theoretical and practical study of a parallel algorithm for generating random tree structures based on Galton-Watson processes, demonstrating significant efficiency improvements in shared memory systems.

Contribution

It introduces a novel parallel generation algorithm for Galton-Watson trees and discusses its implementation challenges and performance in a task-based parallel paradigm.

Findings

Significant efficiency gains in generating large trees.

Successful implementation in shared memory with Cilk.

Theoretical analysis of average-case behavior.

Abstract

In this paper, we study a parallel version of Galton-Watson processes for the random generation of tree-shaped structures. Random trees are useful in many situations (testing, binary search, simulation of physics phenomena,...) as attests more than 49000 citations on Google scholar. Using standard analytic combinatorics, we first give a theoretical, average-case study of the random process in order to evaluate how parallelism can be extracted from this process, and we deduce a parallel generation algorithm. Then we present how it can be implemented in a task-based parallel paradigm for shared memory (here, Intel Cilk). This implementation faces several challenges, among which efficient, thread-safe random bit generation, memory management and algorithmic modifications for small-grain parallelism. Finally, we evaluate the performance of our implementation and the impact of different choices and parameters. We obtain a significant efficiency improvement for the generation of big trees. We also conduct empirical and theoretical studies of the average behaviour of our algorithm.