On clustering bodies: geometry and polyhedral approximation

DOI10.1007/s00454-009-9226-7zbMath1211.52014OpenAlexW2010255669MaRDI QIDQ603849

Peter Gritzmann, Andreas Brieden

Publication date: 8 November 2010

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00454-009-9226-7

zbMATH Keywords

optimizationpolynomial approximationconvex maximizationpermutahedroncomputational convexitygeometric clustering

Mathematics Subject Classification ID

Convex programming (90C25) Computational aspects related to convexity (52B55) Approximation algorithms (68W25)

Related Items (4)

An LP-based \(k\)-means algorithm for balancing weighted point sets ⋮ Constrained clustering via diagrams: a unified theory and its application to electoral district design ⋮ Geometric clustering for the consolidation of farmland and woodland ⋮ Efficient solutions for weight-balanced partitioning problems

Cites Work

• Computational complexity of norm-maximization
• On the complexity of some basic problems in computational convexity. I. Containment problems
• Constrained minimum-\(k\)-star clustering and its application to the consolidation of farmland
• Computational complexity of inner and outer \(j\)-radii of polytopes in finite-dimensional normed spaces
• On Optimal Weighted Balanced Clusterings: Gravity Bodies and Power Diagrams
• Deterministic and randomized polynomial‐time approximation of radii
• Convex Analysis
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