Approximation algorithms for clustering to minimize the sum of diameters
Nordic Journal of Computing
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Clustering to minimize the sum of cluster diameters
Journal of Computer and System Sciences - STOC 2001
Incremental Clustering and Dynamic Information Retrieval
SIAM Journal on Computing
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
A general approach to online network optimization problems
ACM Transactions on Algorithms (TALG)
On clustering to minimize the sum of radii
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
A Randomized Algorithm for Online Unit Clustering
Theory of Computing Systems
Polynomial time approximation schemes for base station coverage with minimum total radii
Computer Networks: The International Journal of Computer and Telecommunications Networking
SIAM Journal on Computing
On Metric Clustering to Minimize the Sum of Radii
Algorithmica - Special Issue: Scandinavian Workshop on Algorithm Theory; Guest Editor: Joachim Gudmundsson
On the online unit clustering problem
ACM Transactions on Algorithms (TALG)
Online clustering with variable sized clusters
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Geometric clustering to minimize the sum of cluster sizes
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Better bounds on online unit clustering
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Computer Science Review
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In Online Sum-Radii Clustering, n demand points arrive online and must be irrevocably assigned to a cluster upon arrival. The cost of each cluster is the sum of a fixed opening cost and its radius, and the objective is to minimize the total cost of the clusters opened by the algorithm. We show that the deterministic competitive ratio of Online Sum-Radii Clustering for general metric spaces is Θ(logn), where the upper bound follows from a primal-dual online algorithm, and the lower bound is valid for ternary Hierarchically Well-Separated Trees (HSTs) and for the Euclidean plane. Combined with the results of (Csirik et al., MFCS 2010), this result demonstrates that the deterministic competitive ratio of Online Sum-Radii Clustering changes abruptly, from constant to logarithmic, when we move from the line to the plane. We also show that Online Sum-Radii Clustering in HSTs is closely related to the Parking Permit problem introduced by (Meyerson, FOCS 2005). Exploiting the relation to Parking Permit, we obtain a lower bound of Ω(loglogn) on the randomized competitive ratio of Online Sum-Radii Clustering in tree metrics. Moreover, we present a simple randomized O(logn)-competitive algorithm, and a deterministic O(loglogn)-competitive algorithm for the fractional version of the problem.