A Lattice Linear Predicate Parallel Algorithm for the Dynamic Programming Problems
Vijay K. Garg · 2022
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 works correctly in a distributed system setting where a processor may use an older value of a variable stored at a different processor.