Date of Award

Spring 6-4-2025

Document Type

Thesis (Undergraduate)

Department

Computer Science

First Advisor

Hsien-Chih Chang

Abstract

We propose a set system of maximum-covering minimum-density partial Steiner trees for planar and minor-free graphs. We show that this system has VC dimension at most h-1 for edge-weighted Kh-minor-free graphs, both directed and undirected. We also consider its geometric interpretation as a range space, proving it to be piercing.

In addition, we demonstrate how one can form a junction tree set system of bounded VC dimension from such Steiner trees. This is motivated by refining the junction tree set cover approach used in Chekuri and Jain's polylogarithmic approximation algorithm for Directed Steiner Forest in planar graphs [CJ25].

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