Algorithm Design & Analysis

This research direction explores the mathematical structures underlying optimization and coordination problems, with applications ranging from UAV routing to theoretical computer science.

A central thread is the study of sweep-covers in partially ordered sets. Sweep-covers generalize pursuit-evasion problems on graphs: given a poset (such as a road network modeled as a tree), how many agents are needed to "sweep" all elements, and how can we enumerate or bound the number of valid sweep strategies? My solo work "Bounds on Sweep-Covers by Raney Numbers" (2020) established novel combinatorial bounds using Raney numbers — a generalization of Catalan numbers — connecting pursuit-evasion to enumerative combinatorics. The follow-up "Bounds on Decorated Sweep Covers in Tree Posets" (2026, with Krawchuk) extends these results to decorated variants with tighter bounds and new structural insights.

On the applied side, my work at the Air Force Research Lab developed multi-epoch planning algorithms for UAV package delivery under stochastic risk (American Controls Conference, 2022). The key challenge is balancing delivery reward against failure probability across sequential missions — a problem we formulated as a constrained stochastic optimization and solved with dynamic programming approaches.

The multi-agent pursuit problem ("Multiple Pursuers Under Partial Information from Sensors") addresses coordination under incomplete observability: how should multiple pursuers on a network allocate effort when sensors provide only partial information about an evader's location?

At the foundational level, "A Relative Church-Turing-Deutsch Thesis from Special Relativity and Undecidability" (2022) investigates the computational power of physical systems, proposing a relativized version of the Church-Turing-Deutsch thesis that accounts for the causal structure of spacetime and undecidability results.

These threads share a focus on deriving provable guarantees and structural results for problems where heuristic or simulation-only approaches are insufficient.