Research
Work & Projects
My work spans combinatorial optimization, algorithm design, and equitable network design — from computational districting to healthcare access modeling. I am especially interested in problems that are not only present rich theoretical challenges, but also arise from real-world needs with significant social impact. Below are my papers and interactive tools built from this research.
If you have an interesting problem that intersects with some of my work and interest, or are looking for a new problem, please reach out by email.
Papers
Coloring of Graphs Avoiding Bicolored Paths of a Fixed Length
Graphs and Combinatorics, 40(1), Art. 11, 2024
We study proper vertex colorings of graphs that avoid bicolored paths of a fixed length — that is, paths whose vertices alternate between exactly two colors. We introduce the Pk-chromatic number sk(G), the minimum number of colors needed for such a coloring. For any graph with maximum degree d ≥ 2 and k ≥ 4, we establish that sk(G) = O(d(k−1)/(k−2)). We also determine exact values of sk for products of cycles and paths when k = 5 and k = 6. The problem generalizes classical star coloring and acyclic coloring and connects chromatic theory with Ramsey-type structural questions.
UAV Routing for Maximum Information Collection under Time Windows
with Melis Boran & Mustafa Tural
FalCom: A Sampling Method for Districting and Hierarchical Facility Location
with Hemanshu Kaul
Chicago Healthcare Network — Optimization-Based Decision Support for Equitable Access
with Hemanshu Kaul & Kim Erwin