Degree Year

2016

Document Type

Thesis

Degree Name

Bachelor of Arts

Department

Mathematics

Advisor(s)

Robert Bosch

Keywords

Quadratic assignment problem, QAP, Discrete optimization, Simulated annealing, Hill climbing, DNA sequence representation

Abstract

We explore methods for drawing a graph of DNA sequences on a digital canvas such that the Euclidean distances between sequences on the canvas suggest the distances between the sequences as calculated from pairwise sequence alignment. We use data from three plant taxa, the genus Castilleja as well as the families Caryophyllaceae and Cactaceae, to test our methods. We discuss different possible measures of the cost of a drawing, and analyze heuristic approaches to the problem including random assignment, greedy assignment, the iterated hill-climber, and simulated annealing. We find that our hill-climbing method tends to return superior drawings. Our simulated annealing method also returns drawings with low costs, but in much less time than the hill-climbing method for large datasets.

Included in

Mathematics Commons

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