eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-08-31
29:1
29:15
10.4230/LIPIcs.ESA.2021.29
article
𝓁_p-Norm Multiway Cut
Chandrasekaran, Karthekeyan
1
https://orcid.org/0000-0002-3421-7238
Wang, Weihang
1
University of Illinois at Urbana-Champaign, IL, USA
We introduce and study 𝓁_p-norm-multiway-cut: the input here is an undirected graph with non-negative edge weights along with k terminals and the goal is to find a partition of the vertex set into k parts each containing exactly one terminal so as to minimize the 𝓁_p-norm of the cut values of the parts. This is a unified generalization of min-sum multiway cut (when p = 1) and min-max multiway cut (when p = ∞), both of which are well-studied classic problems in the graph partitioning literature. We show that 𝓁_p-norm-multiway-cut is NP-hard for constant number of terminals and is NP-hard in planar graphs. On the algorithmic side, we design an O(log² n)-approximation for all p ≥ 1. We also show an integrality gap of Ω(k^{1-1/p}) for a natural convex program and an O(k^{1-1/p-ε})-inapproximability for any constant ε > 0 assuming the small set expansion hypothesis.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol204-esa2021/LIPIcs.ESA.2021.29/LIPIcs.ESA.2021.29.pdf
multiway cut
approximation algorithms