Benchmarking ordering techniques for nonserial dynamic programming

TL;DR

This paper compares five variable ordering algorithms for nonserial dynamic programming, showing that ordering significantly affects run-time and that heuristics like maximum cardinality search and minimum fill-in are most effective for certain sparse discrete optimization problems.

Contribution

It provides a comprehensive benchmarking of ordering algorithms, highlighting the impact of variable ordering on algorithm efficiency and identifying the most effective heuristics for specific problem classes.

Findings

Variable ordering greatly influences run-time performance.

Different orderings are optimal for different problem classes.

Maximum cardinality search and minimum fill-in heuristics perform best among those tested.

Abstract

Five ordering algorithms for the nonserial dynamic programming algorithm for solving sparse discrete optimization problems are compared in this paper. The benchmarking reveals that the ordering of the variables has a significant impact on the run-time of these algorithms. In addition, it is shown that different orderings are most effective for different classes of problems. Finally, it is shown that, amongst the algorithms considered here, heuristics based on maximum cardinality search and minimum fill-in perform best for solving the discrete optimization problems considered in this paper.