{"ID":2848663,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.25664","arxiv_id":"2510.25664","title":"$\\{s,t\\}$-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 $\\{s,t\\}$-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 $\\ell$.","short_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 seq...","url_abs":"https://arxiv.org/abs/2510.25664","url_pdf":"https://arxiv.org/pdf/2510.25664v3","authors":"[\"Kristóf Bérczi\",\"Karthekeyan Chandrasekaran\",\"Tamás Király\",\"Daniel P. Szabo\"]","published":"2025-10-29T16:25:06Z","proceeding":"cs.DS","tasks":"[\"cs.DS\"]","methods":"[]","has_code":false}