$\{s,t\}$-Separating Principal Partition Sequence of Submodular Functions

TL;DR

This paper introduces a new $\

Contribution

It develops the theory and polynomial-time algorithms for the $\

Findings

Provides a polynomial-time algorithm for the $\

paper_type

empirical

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 $\{s,t\}$-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 $\{s,t\}$-separating submodular $k$-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 $k$ and $(s,t)$-connectivity at least $\ell$.