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.
FalCom: A Sampling Method for Districting and Hierarchical Facility Location
with Hemanshu Kaul
We introduce FalCom, the first Markov chain Monte Carlo sampling framework for hierarchical capacitated facility location and districting problems. FalCom extends the spanning-tree proposal of ReCom from single-level political redistricting to multi-level service systems with capacity bounds, demand balance, and facility-aware cut selection. We demonstrate that it scales to graphs of 50,000 basic units — an order of magnitude beyond published hierarchical facility-location methods. Rather than returning a single optimum, FalCom samples ensembles of feasible plans, enabling boundary-robustness maps, essential-vs-substitutable facility analysis, and capacity-utilization distributions that no single-solution method can produce. The framework is validated on synthetic grids and a London Ambulance Service case study and released as an open-source Python library with an interactive visualizer.
UAV Routing for Maximum Information Collection under Time Windows and Energy Consumption
with Melis Boran & Mustafa Tural
We develop an exact convex-optimization framework for UAV reconnaissance routing under time windows, time-dependent rewards, and a nonlinear energy budget. The model jointly selects which targets to visit, the order of visits, the travel speed on each arc, and a separate loitering time at the fixed minimum-power speed, capturing fixed-wing aerodynamics correctly. The resulting mixed-integer nonlinear program is reformulated exactly as a mixed-integer second-order cone program (MISOCP) via a chain of three rotated cones, and is solved at scale by an iterated-local-search matheuristic whose evaluation oracle is a small SOCP. Calibrated on a real-world UAV platform, the approach scales to 200-node Solomon-derived instances.
A Diffusion Model for Political Redistricting
Alaittin Kirtisoglu
ReCom variants, the dominant MCMC methods for political redistricting, are computationally efficient but geometrically blind. We propose a hybrid sampler that complements ReCom with a kernel-aware local-refinement step, based on a graph-diffusion energy formulated as an integer quadratic program. Our results show that the hybrid model admits configurable Laplacian kernels (perimeter, density, demographic) plus a fidelity term that anchors refinement near the current partition. On Iowa precincts, the integer variant reduces mean cut edges by 23.9% vs. ReCom.
Optimization-Based Decision Support for Equitable Expansion of Federally Qualified Health Centers in Chicago
with Hemanshu Kaul
We identify four critical gaps in the current HRSA's granting system for Federally Qualified Health Centers (FQHCs): the absence of location-evaluation tools; an outdated Index of Medical Underservice (IMU) formula; a limited Medically Underserved Area (MUA) designation process; and unmapped referral networks between FQHCs and hospitals. We show how optimization can address each. Integrating a flow-based model into the FalCom sampler, we design catchment areas and hospital-anchored health zones that satisfy HRSA's compliance requirements while balancing demand and capacity, and improving real-time transportation accessibility. We also propose an updated IMU formula, and outline a follow-up effort to map Chicago's physician referral network. To the best of our knowledge, this is the first paper bringing solutions from operations research to the location decisions of FQHCs.