Cut problems form one of the most fundamental classes of problems in algorithmic graph
theory. In this paper, we initiate the algorithmic study of a high-dimensional cut problem. The …

Cut problems form one of the most fundamental classes of problems in algorithmic graph
theory. For instance, the minimum cut, the minimum $ s $-$ t $ cut, the minimum multiway …

This thesis examines three fundamental challenges in computational topology: the
homology localization problem, the minimum bounded chain problem, and the subsurface …

Finding the smallest d-chain with a specific (d− 1)-boundary in a simplicial complex is known
as the Minimum Bounded Chain problem (MBC d). MBC d is NP-hard for all d≥ 2. In this …

Given a simplicial complex with $ n $ simplices, we consider the Connected Subsurface
Recognition (c-SR) problem of finding a subcomplex that is homeomorphic to a given …

Let P be a set of nodes in a wireless network, where each node is modeled as a point in the
plane, and let s ∈ P s∈ P be a given source node. Each node p can transmit information to …

This dissertation is a complexity theoretic study of problems in topology. In the first part, an
open question concerning the approximability of Morse matching is resolved. In the second …

We construct a simply connected 2-complex C embeddable in 3-space such that for any
embedding of C in S 3, any edge contraction forms a minor of the 2-complex not …

We consider three problems on simplicial complexes: the Optimal Bounded Chain Problem,
the Optimal Homologous Chain Problem, and 2-Dim-Bounded-Surface. The Optimal …