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
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
© Copyright 2022 Christopher N. Burgoyne and Travis J. Wheeler