scholarly journals Minimum weight connectivity augmentation for planar straight-line graphs

2019 ◽  
Vol 789 ◽  
pp. 50-63 ◽  
Author(s):  
Hugo A. Akitaya ◽  
Rajasekhar Inkulu ◽  
Torrie L. Nichols ◽  
Diane L. Souvaine ◽  
Csaba D. Tóth ◽  
...  
Keyword(s):  
Minimum Weight ◽  
Line Graphs ◽  
Straight Line ◽  
Connectivity Augmentation

scholarly journals Minimum Weight Connectivity Augmentation for Planar Straight-Line Graphs

2017 ◽  
pp. 204-216 ◽  
Author(s):  
Hugo A. Akitaya ◽  
Rajasekhar Inkulu ◽  
Torrie L. Nichols ◽  
Diane L. Souvaine ◽  
Csaba D. Tóth ◽  
...  
Keyword(s):  
Minimum Weight ◽  
Line Graphs ◽  
Straight Line ◽  
Connectivity Augmentation

Tri-Edge-Connectivity Augmentation for Planar Straight Line Graphs

2009 ◽  
pp. 902-912 ◽  
Author(s):  
Marwan Al-Jubeh ◽  
Mashhood Ishaque ◽  
Kristóf Rédei ◽  
Diane L. Souvaine ◽  
Csaba D. Tóth
Keyword(s):  
Line Graphs ◽  
Edge Connectivity ◽  
Straight Line ◽  
Connectivity Augmentation

Single Bone Straight Line Graphs for the Lower Extremity

1997 ◽  
Vol 342 ◽  
pp. 132???140 ◽  
Author(s):  
James W. Pritchett ◽  
David T. Bortel
Keyword(s):  
Lower Extremity ◽  
Line Graphs ◽  
Straight Line ◽  
Single Bone

Augmenting Planar Straight Line Graphs to 2-Edge-Connectivity

2015 ◽  
pp. 563-564 ◽  
Author(s):  
Hugo Alves Akitaya ◽  
Jonathan Castello ◽  
Yauheniya Lahoda ◽  
Anika Rounds ◽  
Csaba D. Tóth
Keyword(s):  
Line Graphs ◽  
Edge Connectivity ◽  
Straight Line

PARAMETRIC POLYMATROID OPTIMIZATION AND ITS GEOMETRIC APPLICATIONS

2002 ◽  
Vol 12 (05) ◽  
pp. 429-443 ◽  
Author(s):  
NAOKI KATOH ◽  
HISAO TAMAKI ◽  
TAKESHI TOKUYAMA
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Transportation Problem ◽  
Minimum Weight ◽  
Planar Point ◽  
Line Arrangement ◽  
Optimal Bound ◽  
Straight Line ◽  
Point Set ◽  
Multiple Levels

We give an optimal bound on the number of transitions of the minimum weight base of an integer valued parametric polymatroid. This generalizes and unifies Tamal Dey's O(k1/3 n) upper bound on the number of k-sets (and the complexity of the k-level of a straight-line arrangement), David Eppstein's lower bound on the number of transitions of the minimum weight base of a parametric matroid, and also the Θ(kn) bound on the complexity of the at-most-k level (the union of i-levels for i = 1,2,…,k) of a straight-line arrangement. As applications, we improve Welzl's upper bound on the sum of the complexities of multiple levels, and apply this bound to the number of different equal-sized-bucketings of a planar point set with parallel partition lines. We also consider an application to a special parametric transportation problem.

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