Author ORCID Identifier

https://orcid.org/0009-0005-6643-1991

Date of Award

Summer 8-2025

Document Type

Thesis (Ph.D.)

Department or Program

Computer Science

First Advisor

Deeparnab Chakrabarty

Abstract

Finding connected components in undirected hypergraphs—hypergraph connectivity—is a fundamental problem in computer science. It can be framed as a special case of Symmetric Submodular Function Minimization (SSFM), where the objective is to determine if the non-trivial minimizer is zero. This thesis develops an optimal algorithm for hypergraph connectivity within the $\CUT$ query model, where an algorithm probes a subset of vertices to learn the weight of the hyperedges ``cut" by that partition.

Our approach is constructive, culminating in an optimal algorithm for the general problem by first developing the necessary tools for two foundational subproblems. The main contributions of this thesis are: \begin{itemize} \item \textbf{Spanning Forest in Weighted graphs:} An optimal (up to a constant factor), polynomial-time, zero-error algorithm to reconstruct a maximal spanning forest in weighted undirected graphs using $\CUT$ queries. \item \textbf{Partition Learning:} An optimal deterministic algorithm for learning a hypermatching—a problem we term ``partition learning"—using $\RANK$ queries. \item \textbf{Hypergraph Connectivity:} Leveraging these preceding results, we present an optimal, polynomial-time, zero-error algorithm to find the connected components of capacitated hypergraphs using $\CUT$ queries. \end{itemize} Collectively, these results establish a complete and optimal framework for solving hypergraph connectivity in the $\CUT$ query model.

Original Citation

@inproceedings{LiaoC24, author={Liao, Hang and Chakrabarty, Deeparnab}, title={Learning Spanning Forests Optimally in Weighted Undirected Graphs with CUT queries}, pages={785--807}, booktitle={Proc., International Conference on Algorithmic Learning Theory (ALT)}, year={2024} }

@inproceedings{ChakrabartyL24, author={Chakrabarty, Deeparnab and Liao, Hang}, title={Learning Partitions Using Rank Queries}, pages={16--1}, booktitle={Proc., FSTTCS}, year={2024} }

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