Abstract
We introduce and study ℓp-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 ℓp-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 ℓp-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(log 1.5nlog 0.5k) -approximation for all p≥ 1. We also show an integrality gap of Ω (k1-1/p) for a natural convex program and an O(k1-1/p-ϵ) -inapproximability for any constant ϵ> 0 assuming the small set expansion hypothesis.
Original language | English (US) |
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Pages (from-to) | 2667-2701 |
Number of pages | 35 |
Journal | Algorithmica |
Volume | 84 |
Issue number | 9 |
Early online date | May 23 2022 |
DOIs | |
State | Published - Sep 2022 |
Keywords
- Approximation algorithms
- Multiway cut
ASJC Scopus subject areas
- General Computer Science
- Computer Science Applications
- Applied Mathematics