Nested Dataflow Algorithms for Dynamic Programming Recurrences with more than O(1) Dependency

TL;DR

This paper introduces a novel nested dataflow algorithm for dynamic programming recurrences with more than O(1) dependencies, providing the first sublinear-time solution for the general GAP problem and improving existing algorithms.

Contribution

It develops the first work-efficient, sublinear-time algorithm for the general GAP problem using nested dataflow, and enhances time bounds for classic algorithms in 1D and GAP problems.

Findings

First sublinear-time GAP algorithm based on nested dataflow

Improved time bounds for classic 1D and GAP algorithms

Answer to the open question posed by Galil and Park in 1994

Abstract

Dynamic programming problems have wide applications in real world and have been studied extensively in both serial and parallel settings. In 1994, Galil and Park developed work-efficient and sublinear-time algorithms for several important dynamic programming problems based on the closure method and matrix product method. However, in the same paper, they raised an open question whether such an algorithm exists for the general GAP problem. % In this paper, we answer their question by developing the first work-efficient and sublinear-time GAP algorithm based on the closure method and Nested Dataflow method. % We also improve the time bounds of classic work-efficient, cache-oblivious and cache-efficient algorithms for the 1D problem and GAP problem, respectively.