Geometric clustering to minimize the sum of cluster sizes

Authors:
Vittorio Bilò;Ioannis Caragiannis;Christos Kaklamanis;Panagiotis Kanellopoulos
Affiliations:
Dipartimento di Matematica “Ennio De Giorgi”, Università di Lecce, Provinciale Lecce-Arnesano, Lecce, Italy;Research Academic Computer Technology Institute &, Department of Computer Engineering and Informatics, University of Patras, Rio, Greece;Research Academic Computer Technology Institute &, Department of Computer Engineering and Informatics, University of Patras, Rio, Greece;Research Academic Computer Technology Institute &, Department of Computer Engineering and Informatics, University of Patras, Rio, Greece
Venue:
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Year:
2005

Citing 12
Cited 19

Geometric clusterings

Journal of Algorithms
Approximation schemes for Euclidean k-medians and related problems

STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Polynomial-time approximation schemes for geometric graphs

SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for metric facility location and k-Median problems using the primal-dual schema and Lagrangian relaxation

Journal of the ACM (JACM)
Approximating min-sum k-clustering in metric spaces

STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Polynomial-time approximation schemes for geometric min-sum median clustering

Journal of the ACM (JACM)
Approximate clustering via core-sets

STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
A constant-factor approximation algorithm for the k-median problem

Journal of Computer and System Sciences - STOC 1999
Approximation algorithms for clustering to minimize the sum of diameters

Nordic Journal of Computing
Approximation schemes for clustering problems

Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Clustering to minimize the sum of cluster diameters

Journal of Computer and System Sciences - STOC 2001
Polynomial time approximation schemes for base station coverage with minimum total radii

Computer Networks: The International Journal of Computer and Telecommunications Networking

Minimum-cost coverage of point sets by disks

Proceedings of the twenty-second annual symposium on Computational geometry
Algorithms for two-box covering

Proceedings of the twenty-second annual symposium on Computational geometry
On clustering to minimize the sum of radii

Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Power Assignment Problems in Wireless Communication: Covering Points by Disks, Reaching few Receivers Quickly, and Energy-Efficient Travelling Salesman Tours

DCOSS '08 Proceedings of the 4th IEEE international conference on Distributed Computing in Sensor Systems
On Metric Clustering to Minimize the Sum of Radii

SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Finding Facilities Fast

ICDCN '09 Proceedings of the 10th International Conference on Distributed Computing and Networking
Cheap or Flexible Sensor Coverage

DCOSS '09 Proceedings of the 5th IEEE International Conference on Distributed Computing in Sensor Systems
Locating facilities on a network to minimize their average service radius

ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Multi cover of a polygon minimizing the sum of areas

WALCOM'11 Proceedings of the 5th international conference on WALCOM: algorithms and computation
Power assignment problems in wireless communication: Covering points by disks, reaching few receivers quickly, and energy-efficient travelling salesman tours

Ad Hoc Networks
Connecting a set of circles with minimum sum of radii

WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Partitioning the nodes of a graph to minimize the sum of subgraph radii

ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Radar placement along banks of river

Journal of Global Optimization
Shifting strategy for geometric graphs without geometry

Journal of Combinatorial Optimization
On Clustering to Minimize the Sum of Radii

SIAM Journal on Computing
Online sum-radii clustering

MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
A note on multicovering with disks

Computational Geometry: Theory and Applications
A mixed breadth-depth first strategy for the branch and bound tree of Euclidean k-center problems

Computational Optimization and Applications
A constant-factor approximation for multi-covering with disks

Proceedings of the twenty-ninth annual symposium on Computational geometry

Quantified Score

Hi-index	0.00

Visualization

Abstract

We study geometric versions of the min-size k-clustering problem, a clustering problem which generalizes clustering to minimize the sum of cluster radii and has important applications. We prove that the problem can be solved in polynomial time when the points to be clustered are located on a line. For Euclidean spaces of higher dimensions, we show that the problem is NP-hard and present polynomial time approximation schemes. The latter result yields an improved approximation algorithm for the related problem of k-clustering to minimize the sum of cluster diameters.