A Lattice Linear Predicate Parallel Algorithm for the Dynamic Programming Problems

TL;DR

This paper extends the parallel Lattice Linear Predicate algorithm to solve various dynamic programming problems efficiently, including constrained versions, using only read-write atomicity.

Contribution

It introduces a parallel LLP algorithm tailored for dynamic programming problems and their lattice-linear constrained variants.

Findings

Successfully solves longest subsequence, optimal binary search tree, and knapsack problems

Handles lattice-linear constraints in dynamic programming

Operates with only read-write atomicity

Abstract

It has been shown that the parallel Lattice Linear Predicate (LLP) algorithm solves many combinatorial optimization problems such as the shortest path problem, the stable marriage problem and the market clearing price problem. In this paper, we give the parallel LLP algorithm for many dynamic programming problems. In particular, we show that the LLP algorithm solves the longest subsequence problem, the optimal binary search tree problem, and the knapsack problem. Furthermore, the algorithm can be used to solve the constrained versions of these problems so long as the constraints are lattice linear. The parallel LLP algorithm requires only read-write atomicity and no higher-level atomic instructions.