LASSO: Listing All Subset Sums Obediently for Evaluating Unbounded Subset Sums

Author

Christopher N. Burgoyne, University of MontanaFollow
Travis J. Wheeler, University of Montana

Year of Award

2022

Document Type

Thesis

Degree Type

Master of Science (MS)

Degree Name

Computer Science

Department or School/College

Computer Science

Committee Chair

Travis Wheeler

Commitee Members

Jesse Johnson, Cory Palmer

Keywords

Unbounded subset sum, Subset sum, Knapsack, Combinatorics

Publisher

University of Montana

Subject Categories

Computer Sciences | Discrete Mathematics and Combinatorics | Theory and Algorithms

Abstract

In this study we present a novel algorithm, LASSO, for solving the unbounded and bounded subset sum problem. The LASSO algorithm was designed to solve the unbounded SSP quickly and to return all subsets summing to a target sum. As speed was the highest priority, we benchmarked the run time performance of LASSO against implementations of some common approaches to the bounded SSP, as well as the only comparable implementation for solving the unbounded SSP that we could find. In solving the bounded SSP, our algorithm had a significantly faster run time than the competing algorithms when the target sum returned at least one subset. When the target returned no subsets, LASSO had a poorer run time growth rate than the competing algorithms solving bounded subset sum. For solving the USSP LASSO was significantly faster than the only comparable algorithm for this problem, both in run time and run time growth rate.

Recommended Citation

Burgoyne, Christopher N. and Wheeler, Travis J., "LASSO: Listing All Subset Sums Obediently for Evaluating Unbounded Subset Sums" (2022). Graduate Student Theses, Dissertations, & Professional Papers. 11943.
https://scholarworks.umt.edu/etd/11943