$\{s,t\}$-Separating Principal Partition Sequence of Submodular Functions
Abstract
Narayanan showed the existence of the principal partition sequence of a submodular function, a structure with numerous applications in areas such as clustering, fast algorithms, and approximation algorithms. In this work, motivated by two applications, we develop a theory of -separating principal partition sequence of a submodular function. We define this sequence, show its existence, and design a polynomial-time algorithm to construct it. We show two applications: (1) approximation algorithm for the -separating submodular -partitioning problem for monotone and posimodular functions and (2) polynomial-time algorithm for the hypergraph orientation problem of finding an orientation that simultaneously has strong connectivity at least and -connectivity at least .
Cite
@article{arxiv.2510.25664,
title = {$\{s,t\}$-Separating Principal Partition Sequence of Submodular Functions},
author = {Kristóf Bérczi and Karthekeyan Chandrasekaran and Tamás Király and Daniel P. Szabo},
journal= {arXiv preprint arXiv:2510.25664},
year = {2026}
}