Urban Planning: From Grids to Graphs
University
Shawnee State University
Major
Mathematics
Student Type
Graduate Student
Presentation Types
Oral Presentation (Live)
Keywords:
Improper clique coloring, discrete optimization, graph theory, urban planning
Abstract
In a world where graphs are used to model relationships in social networks, as a foundation for neural-networks in Large Language Models, and to help cell phones find how long it will take to get from San Diego to Los Angeles, what if we could also use them to help lay the foundations for effective city planning? The original definition of the Urban Planning problem starts with a square grid where we look to optimally place residential and commercial properties subject to specific criteria. In this presentation, we will examine solutions to the Urban Planning Problem for n × n grids and extend this concept to the more general setting of proper and improper clique colorings in graphs. We seek to demonstrate the optimal urban planning score in each scenario while exploring this unique application of discrete optimization.
Human and Animal Subjects
no
Faculty Mentor Name
R. Duane Skaggs
Faculty Mentor Title
Professor
Faculty Mentor Department
Mathematical Sciences
Recommended Citation
Copenhaver, Daniel J., "Urban Planning: From Grids to Graphs" (2026). Celebration of Scholarship. 4.
https://digitalcommons.shawnee.edu/cos/2026/dayone/4
Urban Planning: From Grids to Graphs
In a world where graphs are used to model relationships in social networks, as a foundation for neural-networks in Large Language Models, and to help cell phones find how long it will take to get from San Diego to Los Angeles, what if we could also use them to help lay the foundations for effective city planning? The original definition of the Urban Planning problem starts with a square grid where we look to optimally place residential and commercial properties subject to specific criteria. In this presentation, we will examine solutions to the Urban Planning Problem for n × n grids and extend this concept to the more general setting of proper and improper clique colorings in graphs. We seek to demonstrate the optimal urban planning score in each scenario while exploring this unique application of discrete optimization.