Publications

Publications and Preprints

An asterisk (*) denotes a coauthor who was an undergraduate coauthor for some or all of the work!

• Circulant TSP: Vertices of the Edge-Length Polytope and Superpolynomial Lower Bounds.  To appear in Discrete Applied Mathematics.
• Defying Gravity or Failing to Launch, Measuring the Profitability of Broadway musicals for investors, with Allan Detsky and Christopher Kopac*.  To appear in Significance.
• The Two-Stripe Symmetric Circulant TSP is in P [Full Journal Submission, with lots and lots of Figures and proofs!], with Billy Jin and David P. Williamson. Mathematical Programming, April 2025.
• Circulant TSP Special Cases: Easily-Solvable Cases and Improved Approximations, with Austin Beal*, Yacine Bouabida*, and Asta Rustad*.  Operations Research Letters, 2024.
• Scorigami: Simulating the Distribution and Assessing the Rarity of National Football League Scores, with Liam Moyer*, Jameson Railey*, and Andrew Daw.  Proceedings of the Winter Simulation Conference 2024.
• GILP: An Interactive Tool for Visualizing the Simplex Algorithm, with Henry W. Robbins*, David B. Shmoys, and David P. Williamson.  SIGCSE ‘2023.
• The Circlet Inequalities: A New, Circulant-Based Facet-Defining Inequality for the TSP, with David P. Williamson.  Mathematics of Operations Research 48(1), 2023.
• The Two-Stripe Symmetric Circulant TSP is in P [Extended Abstract], with Billy Jin and David P. Williamson.  IPCO 2022.
• Semidefinite Programming Relaxations of the Traveling Salesman Problem and Their Integrality Gaps, with David P. Williamson.  Mathematics of Operations Research 47(1), 2022.
• Root Cones and the Resonance Arrangement, with Karola Mészáros and T. Kyle Petersen.  Electronic Journal of Combinatorics 28(1), 2021.
• An Automated Tool for Optimal Classroom Seating Assignment with Social Distancing Constraints, with Kyle Greenberg*, Trey Hensel*, Jody Zhu*, Sander Aarts, and David B. Shmoys. Proceedings of the IISE Annual Conference & Expo 2021.
• Subtour Elimination Constraints Imply a Matrix-Tree Theorem SDP Constraint for the TSP, with David P. Williamson. Operations Research Letters 48(3):245-248, 2020.
• Mathematics of Nested Districts: The Case of Alaska, with Sophia Caldera*, Daryl DeFord, Moon Duchin, and Cara Nix*. (Based on work with undergraduate students at the 2018 Voting Rights Data Institute.)  Statistics and Public Policy, 2020.  See also the project GitHub.
• Characterizing the Integrality Gap of the Subtour LP for the Circulant Traveling Salesman Problem, with David P. Williamson. SIAM Journal on Discrete Mathematics 33(4):2452–2478, 2019.
• The Unbounded Integrality Gap of a Semidefinite Relaxation of the Traveling Salesman Problem, with David P. Williamson. SIAM Journal on Optimization 28:2073-2096, 2018.
• The Mean(est) Voting System, with David Lingenbrink and Michael Orrison.  Math and Voting special issue of Math Horizons, 2016. (Based on undergraduate work at Harvey Mudd)
• Permutation Patterns in Latin Squares, with Michael Earnest. The Australasian Journal of Combinatorics, 2014. (Based on undergraduate work at the ETSU Math REU)
• Logarithmic Representability of Integers as k-Sums, with Anant Godbole, Vince Lyzinski, and Yan Zhuang.  Erdos Centennial Conference volume of Integers, 2013. (Based on undergraduate work at the ETSU Math REU)

I have several internal papers within industry.  Details are available on request.