scholarly journals On 2-Site Voronoi Diagrams under Geometric Distance Functions

2011 ◽  
Author(s):  
Gill Barequet ◽  
Matthew T. Dickerson ◽  
David Eppstein ◽  
David Hodorkovsky ◽  
Kira Vyatkina
Keyword(s):  
Voronoi Diagrams ◽  
Distance Functions ◽  
Geometric Distance

scholarly journals On 2-Site Voronoi Diagrams Under Geometric Distance Functions

2013 ◽  
Vol 28 (2) ◽  
pp. 267-277
Author(s):  
Gill Barequet ◽  
Matthew Dickerson ◽  
David Eppstein ◽  
David Hodorkovsky ◽  
Kira Vyatkina
Keyword(s):  
Voronoi Diagrams ◽  
Distance Functions ◽  
Geometric Distance

scholarly journals Voronoi Diagrams in Higher Dimensions under Certain Polyhedral Distance Functions

1998 ◽  
Vol 19 (4) ◽  
pp. 485-519 ◽  
Author(s):  
J.-D. Boissonnat ◽  
M. Sharir ◽  
B. Tagansky ◽  
M. Yvinec
Keyword(s):  
Voronoi Diagrams ◽  
Higher Dimensions ◽  
Distance Functions

scholarly journals Voronoi diagrams for convex polygon-offset distance functions

2001 ◽  
Vol 25 (2) ◽  
pp. 271-291 ◽  
Author(s):  
G. Barequet ◽  
M. T. Dickerson ◽  
M. T. Goodrich
Keyword(s):  
Convex Polygon ◽  
Voronoi Diagrams ◽  
Distance Functions ◽  
Offset Distance

scholarly journals Voronoi Diagrams of Lines in 3-Space Under Polyhedral Convex Distance Functions

1998 ◽  
Vol 29 (2) ◽  
pp. 238-255 ◽  
Author(s):  
L.Paul Chew ◽  
Klara Kedem ◽  
Micha Sharir ◽  
Boaz Tagansky ◽  
Emo Welzl
Keyword(s):  
Voronoi Diagrams ◽  
Distance Functions ◽  
Polyhedral Convex ◽  
Convex Distance Functions

Malmquist and Hicks–Moorsteen Productivity Indexes for Clusters Performance Evaluation

2016 ◽  
Vol 15 (05) ◽  
pp. 1015-1053 ◽  
Author(s):  
Diogo Cunha Ferreira ◽  
Rui Cunha Marques
Keyword(s):  
Monte Carlo ◽  
Operational Research ◽  
Geometric Mean ◽  
Radial Distance ◽  
Efficient Frontier ◽  
Distance Functions ◽  
Cluster Performance ◽  
Geometric Distance ◽  
General Cluster ◽  
Over Time

Measuring the performance of clusters characterized by the unbalancedeness and units with no correspondence in other clusters (“uncorrespondencedeness”) has not achieved the desired attention in the literature. Particularly, the operational research has been almost exclusively focused on performance evolution over time, where clusters are generally balanced and the units repeat themselves over these groups. Such analysis has been based on the Malmquist and the Hicks–Moorsteen indexes (MI and HMI), which are solely based on Shephard’s radial distance functions and do not account for all inefficiency sources. Making use of the so-called geometric distance functions (GDFs) and the GDF-based MI, we propose a generalization of the Hicks–Moorsteen index (HMI), based on targets instead of distances to the efficient frontier, allowing the introduction of all inefficiency sources in the productivity model. Moreover, we propose a Monte Carlo-based framework to achieve the pseudo-corresponding units for general cluster performance analysis. This framework is then a generalization of the conventional performance evolution over time. Then, we show that the HMI can be decomposed into economically meaningful indexes and can be rewritten as the geometric mean of the input and the output-oriented MIs. Given these conclusions and our proposed framework, the employment of the HMI to the general clusters analysis is straightforward. Other economically meaningful conclusions are also obtained in this paper.

scholarly journals Kinetic Voronoi Diagrams and Delaunay Triangulations under Polygonal Distance Functions

2015 ◽  
Vol 54 (4) ◽  
pp. 871-904 ◽  
Author(s):  
Pankaj K. Agarwal ◽  
Haim Kaplan ◽  
Natan Rubin ◽  
Micha Sharir
Keyword(s):  
Voronoi Diagrams ◽  
Distance Functions ◽  
Delaunay Triangulations
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