scholarly journals The Complexity of the Simultaneous Cluster Problem

2014 ◽  
Vol 18 (1) ◽  
pp. 1-34 ◽  
Author(s):  
Zhentao Li ◽  
Manikandan Narayanan ◽  
Adrian Vetta
Keyword(s):  
Cluster Problem

scholarly journals On the honeycomb conjecture for Robin Laplacian eigenvalues

2019 ◽  
Vol 21 (02) ◽  
pp. 1850007 ◽  
Author(s):  
Dorin Bucur ◽  
Ilaria Fragalà
Keyword(s):  
Torsional Rigidity ◽  
Cluster Problem ◽  
Laplacian Eigenvalues ◽  
Convexity Assumption ◽  
Robin Laplacian ◽  
Cheeger Sets ◽  
Optimal Cluster

We prove that the optimal cluster problem for the sum/the max of the first Robin eigenvalue of the Laplacian, in the limit of a large number of convex cells, is asymptotically solved by (the Cheeger sets of) the honeycomb of regular hexagons. The same result is established for the Robin torsional rigidity. In the specific case of the max of the first Robin eigenvalue, we are able to remove the convexity assumption on the cells.

scholarly journals The cluster problem revisited

2013 ◽  
Vol 58 (3) ◽  
pp. 429-438 ◽  
Author(s):  
Achim Wechsung ◽  
Spencer D. Schaber ◽  
Paul I. Barton
Keyword(s):  
Cluster Problem

scholarly journals Numerical Study of Semidefinite Bounds for the k-cluster Problem

2010 ◽  
Vol 36 ◽  
pp. 399-406 ◽  
Author(s):  
Jérôme Malick ◽  
Frédéric Roupin
Keyword(s):  
Numerical Study ◽  
Cluster Problem

scholarly journals 3n+lquantum number in the cluster problem

1996 ◽  
Vol 54 (1) ◽  
pp. 670-676 ◽  
Author(s):  
Erik Koch
Keyword(s):  
Cluster Problem

A cluster problem as defined by nearest neighbours

1999 ◽  
Vol 27 (4) ◽  
pp. 843-851 ◽  
Author(s):  
E. G. Enns ◽  
P. F. Ehlers ◽  
T. Misi
Keyword(s):  
Cluster Problem ◽  
Nearest Neighbours
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