Approximation algorithms for clustering to minimize the sum of diameters
Nordic Journal of Computing
Clustering to minimize the sum of cluster diameters
Journal of Computer and System Sciences - STOC 2001
Minimum-cost coverage of point sets by disks
Proceedings of the twenty-second annual symposium on Computational geometry
Polynomial time approximation schemes for base station coverage with minimum total radii
Computer Networks: The International Journal of Computer and Telecommunications Networking
Geometric clustering to minimize the sum of cluster sizes
ESA'05 Proceedings of the 13th annual European conference on Algorithms
The 2-radius and 2-radiian problems on trees
Theoretical Computer Science
Locating facilities on a network to minimize their average service radius
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
On Clustering to Minimize the Sum of Radii
SIAM Journal on Computing
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Let G=(V,E) denote a weighted graph of n nodes and m edges, and let G[ V ′ ] denote the subgraph of G induced by a subset of nodes V′⊆V. The radius of G[ V ′ ] is the maximum length of a shortest path in G[ V ′ ] emanating from its center (i.e., a node of G[ V ′ ] of minimum eccentricity). In this paper, we focus on the problem of partitioning the nodes of G into exactly p non-empty subsets, so as to minimize the sum of the induced subgraph radii. We show that this problem – which is of significance in facility location applications – is NP-hard when p is part of the input, but for a fixed constant p 2 it can be solved in O(n2p/p!) time. Moreover, for the notable case p=2, we present an efficient O(mn2+n3 logn) time algorithm.