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Dissertation defense, April 9: Abir Islam

April 3, 2025

Student Name: Abir Islam
Program: PhD Computer Science
Date: Wednesday 4/9/25
Time: 10:00 am
Place: Moses Lab - FEC 3300
Committee Chair: Dr. Jared Saia

"Algorithms to estimate contours: two applications of analytical tools in differential geometry and topology"

by Mohammad Abirul Islam

B.S., Mathematics, National University of Singapore, 2014
Ph.D., Computer Science, University of New Mexico, 2025

Abstract

We extend a set of mathematical concepts to develop and analyze dis- tributed algorithms in the interface of robotics and computational geom- etry. These include notions needed to define and analyze complexities of angle turned and distance traversed by robots executing geometric algo- rithms. We then present two use cases that make use of these analytical tools where local information can be obtained (e.g. via sensors) about an otherwise unknown surface to compute quantities of interest. First, we develop the Sketch Algorithm which estimates the boundary of any unknown contour and is asymptotically optimal in terms of distance tra- versed and angle turned. Second, we present experimental field work that validates the Sketch Algorithm. Finally, we propose an approach to find multiple sources of a surface with potential applications to approximate it via contours whose total rotations are bounded by a constant.