Dr. Thomas R. Cameron, Assistant Professor, Davidson College
January 24, 2020
Walker Hall, Room 103A
This talk is free and open to the public.
The linear ordering problem is one of the classical combinatorial optimization problems, which attempts to form an optimal ranking of a collection of objects. Often, there is more than one optimal ranking, which leaves room to question how meaningful these rankings are. The rankability problem attempts to quantify a datasets inherent ability to produce a meaningful ranking of items. In 2018, Anderson et al. proposed a measure of rankability that uses integer programming to model the minimum number of changes necessary for a given data set to have a unique optimal ranking. Integer
programming problems are often NP-Hard, and this particular model has practical limitations that restrict the type of data which can be analyzed.
In this talk, we present a rankability measure that is based on a spectral-degree characterization of acyclic tournament graphs. As an eigenvalue problem, our measure has O(n^3) complexity, where n is the number of vertices in the graph, and guaranteed backward stability. Finally, we use our measure to analyze the rankability of data sets from chess, college rankings, and football.
Thomas R. Cameron is a visiting assistant professor of Mathematics and Computer Science at Davidson College. He is a passionate mathematics teacher and scholar whose interests lie at the intersection of algebraic graph theory, data science and numerical analysis. He currently lives in Davidson, N.C., with his wife Kate, son Hudson, and daughter Emmy.
This event is sponsored by the Department of Mathematical Sciences. Please contact Quinn Morris firstname.lastname@example.org or Travis Weiland email@example.com or visit: https://mathsci.appstate.edu/activities-outreach/department-colloquia to view more information and see other upcoming events.
About the Department of Mathematical Sciences
The Department of Mathematical Sciences offers undergraduate degrees in actuarial science and mathematics, with concentrations in business, computation, life sciences, physical sciences, secondary teaching and statistics, plus a general, self-designed concentration. The department also offers the Master of Arts in mathematics, with concentrations in college teaching and secondary teaching. Learn more at https://mathsci.appstate.edu.