Author ORCID Identifier
Date of Award
Spring 5-31-2026
Document Type
Thesis (Undergraduate)
Department
Computer Science
First Advisor
Deeparnab Chakrabarty
Abstract
Hypergraphs provide a flexible model for higher-order relationships, but their variable edge sizes create significant challenges for sublinear algorithms. This thesis investigates sublinear algorithms for estimating the average degree of a hypergraph under natural query models. In the Base Model, we develop estimators for k-uniform and up to k-uniform hypergraphs based on assigning each edge to a unique minimum-degree vertex. In the Standard Model, where random edge queries are available, we show how to simulate degree-proportional vertex sampling and apply weighted sum estimation techniques.
The main algorithmic result is an estimator for general hypergraphs with query complexity Oε(n2/3). The algorithm partitions edges into small and big edges, handles the two sources of variance sep- arately, and combines the resulting estimates to approximate the average degree. We also prove query lower bounds via Yao’s Lemma, demonstrating limitations of these models and highlighting the role of hidden dense substructures in hypergraph estimation.
Recommended Citation
LaPorte, Cooper, "Sublinear Algorithms for Average Degree Estimation in Hypergraphs" (2026). Computer Science Senior Theses. 64.
https://digitalcommons.dartmouth.edu/cs_senior_theses/64
