scholarly journals Induced acyclic tournaments in random digraphs: Sharp concentration, thresholds and algorithms

2014 ◽  
Vol 34 (3) ◽  
pp. 467 ◽  
Author(s):  
Kunal Dutta ◽  
C.R. Subramanian
Keyword(s):  
Random Digraphs ◽  
Sharp Concentration

Sharp Concentration of the Number of Submaps in Random Planar Triangulations

COMBINATORICA ◽  
2003 ◽  
Vol 23 (3) ◽  
pp. 467-486 ◽  
Author(s):  
Zhicheng Gao* ◽  
Nicholas C. Wormald†
Keyword(s):  
Sharp Concentration

scholarly journals Random walk on sparse random digraphs

2017 ◽  
Vol 170 (3-4) ◽  
pp. 933-960 ◽  
Author(s):  
Charles Bordenave ◽  
Pietro Caputo ◽  
Justin Salez
Keyword(s):  
Random Walk ◽  
Random Digraphs

Nucleation controlled reaction of Cu3Si in the field of sharp concentration gradient

2016 ◽  
Vol 112 ◽  
pp. 315-325 ◽  
Author(s):  
M. Ibrahim ◽  
Z. Balogh-Michels ◽  
P. Stender ◽  
D. Baither ◽  
G. Schmitz
Keyword(s):  
Concentration Gradient ◽  
Sharp Concentration

Strong K-Connectivity in Digraphs and Random Digraphs

1981 ◽  
Author(s):  
John H. Reif ◽  
Paul G. Spirakis
Keyword(s):  
Random Digraphs

scholarly journals Packing and counting arbitrary Hamilton cycles in random digraphs

2018 ◽  
Vol 54 (3) ◽  
pp. 499-514
Author(s):  
Asaf Ferber ◽  
Eoin Long
Keyword(s):  
Hamilton Cycles ◽  
Random Digraphs

scholarly journals PageRank on inhomogeneous random digraphs

2020 ◽  
Vol 130 (4) ◽  
pp. 2312-2348
Author(s):  
Jiung Lee ◽  
Mariana Olvera-Cravioto
Keyword(s):  
Random Digraphs

On the size of a random sphere of influence graph

1999 ◽  
Vol 31 (3) ◽  
pp. 596-609 ◽  
Author(s):  
T. K. Chalker ◽  
A. P. Godbole ◽  
P. Hitczenko ◽  
J. Radcliff ◽  
O. G. Ruehr
Keyword(s):  
Upper And Lower Bounds ◽  
Exponential Inequality ◽  
Nearest Neighbour ◽  
Expected Number ◽  
Spheres Of Influence ◽  
Influence Graph ◽  
Influence Graphs ◽  
Sphere Of Influence ◽  
Proximity Graph ◽  
Sharp Concentration

We approach sphere of influence graphs (SIGs) from a probabilistic perspective. Ordinary SIGs were first introduced by Toussaint as a type of proximity graph for use in pattern recognition, computer vision and other low-level vision tasks. A random sphere of influence graph (RSIG) is constructed as follows. Consider n points uniformly and independently distributed within the unit square in d dimensions. Around each point, Xi, draw an open ball (‘sphere of influence’) with radius equal to the distance to Xi's nearest neighbour. Finally, draw an edge between two points if their spheres of influence intersect. Asymptotically exact values for the expected number of edges in a RSIG are determined for all values of d; previously, just upper and lower bounds were known for this quantity. A modification of the Azuma-Hoeffding exponential inequality is employed to exhibit the sharp concentration of the number of edges around its expected value.

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