Fast and Work-Optimal Parallel Algorithms for Predicate Detection

TL;DR

This paper introduces the first work-optimal parallel algorithms for predicate detection in distributed systems, significantly improving time, work, and space complexities over previous methods.

Contribution

It presents deterministic and randomized work-optimal parallel algorithms for predicate detection with improved efficiency and space complexity.

Findings

Deterministic algorithm: O(mn) time, O(mn^2) work.

Randomized algorithm: (mn)^{1/2 + o(1)} time, ilde{O}(mn^2) work.

Space complexity reduced to O(mn^2) from O(m^2n^2).

Abstract

Recently, the predicate detection problem was shown to be in the parallel complexity class NC. In this paper, we give the first work-optimal parallel algorithm to solve the predicate detection problem on a distributed computation with $n$ processes and at most $m$ states per process. The previous best known parallel predicate detection algorithm, ParallelCut, has time complexity $O(\log mn)$ and work complexity $O(m^3n^3\log mn)$. We give two algorithms, a deterministic algorithm with time complexity $O(mn)$ and work complexity $O(mn^2)$, and a randomized algorithm with time complexity $(mn)^{1/2 + o(1)}$ and work complexity $\tilde{O}(mn^2)$. Furthermore, our algorithms improve upon the space complexity of ParallelCut. Both of our algorithms have space complexity $O(mn^2)$ whereas ParallelCut has space complexity $O(m^2n^2)$.