Author ORCID Identifier

https://orcid.org/0000-0001-6787-7286

Date of Award

2026

Document Type

Thesis (Ph.D.)

Department or Program

Computer Science

First Advisor

Deeparnab Chakrabarty

Abstract

Center-based metric k-clustering is a rich class of well-studied optimization problems. These include the classical k-center, k-median, and k-means problems. In all these problems, a client set C and a set F of candidate facilities live in a metric space. We are required to pick or "open" k facilities S ⊆ F to minimize some objective function, potentially subject to further constraints on S. Such problems are NP-hard, which has encouraged a long line of research in approximation algorithms for them.

In this thesis, I present research on center-based k-clustering in scenarios where either the facility set F or the metric d are implicit or uncertain. This is modeled in a few different ways. For example, the algorithm can have very limited access to an exponentially large F, or be constrained to account for facility closures post-output---these are respectively referred to as continuous and fault-tolerant clustering. In another model called aggregate clustering, which aims to model seasonal road closures, a few different metrics d1,...,dT on the same point-set must be accounted for by the same solution.

I study these various models and conclude that, in some special cases of the uncertain models, the approximability is closer to that of the classical models. The round-or-cut method, and LP rounding in general, emerge as useful tools for designing algorithms in this area. It also becomes useful to understand the sensitivity of clustering objectives to small changes in the underlying metric, since a collection of "similar" metrics is a special case of aggregate clustering.

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