scholarly journals The Crossing Number of a Projective Graph is Quadratic in the Face–Width

10.37236/770 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
I. Gitler ◽  
P. Hliněný ◽  
J. Leaños ◽  
G. Salazar
Keyword(s):  
Approximation Algorithm ◽  
Projective Plane ◽  
Crossing Number ◽  
Orientable Surface ◽  
Constant Factor ◽  
Bounded Degree ◽  
Face Width ◽  
Projective Graph ◽  
The Face ◽  
Large Face

We show that for each integer $g\geq0$ there is a constant $c_g > 0$ such that every graph that embeds in the projective plane with sufficiently large face–width $r$ has crossing number at least $c_g r^2$ in the orientable surface $\Sigma_g$ of genus $g$. As a corollary, we give a polynomial time constant factor approximation algorithm for the crossing number of projective graphs with bounded degree.

scholarly journals The crossing number of a projective graph is quadratic in the face–width

2007 ◽  
Vol 29 ◽  
pp. 219-223 ◽  
Author(s):  
Isidoro Gitler ◽  
Petr Hliněný ◽  
Jesus Leaños ◽  
Gelasio Salazar
Keyword(s):  
Crossing Number ◽  
Face Width ◽  
Projective Graph ◽  
The Face

A cycle cover of a 2-edge-connected graph embedded with large face-width on an orientable surface

2016 ◽  
Vol 212 (1) ◽  
pp. 219-235
Author(s):  
Dengju Ma ◽  
Han Ren
Keyword(s):  
Connected Graph ◽  
Orientable Surface ◽  
Cycle Cover ◽  
Face Width ◽  
Large Face

scholarly journals Asymptotic Enumeration of Labelled Graphs by Genus

10.37236/500 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Edward A. Bender ◽  
Zhicheng Gao
Keyword(s):  
Orientable Surface ◽  
Asymptotic Formulas ◽  
Asymptotic Enumeration ◽  
Connected Graphs ◽  
Face Width ◽  
Surface Maps ◽  
Connected Surface ◽  
Labelled Graphs ◽  
Large Face

We obtain asymptotic formulas for the number of rooted 2-connected and 3-connected surface maps on an orientable surface of genus $g$ with respect to vertices and edges simultaneously. We also derive the bivariate version of the large face-width result for random 3-connected maps. These results are then used to derive asymptotic formulas for the number of labelled $k$-connected graphs of orientable genus $g$ for $k\le3$.

scholarly journals Constant factor approximation algorithm for TSP satisfying a biased triangle inequality

2017 ◽  
Vol 657 ◽  
pp. 111-126 ◽  
Author(s):  
Usha Mohan ◽  
Sivaramakrishnan Ramani ◽  
Sounaka Mishra
Keyword(s):  
Approximation Algorithm ◽  
Triangle Inequality ◽  
Constant Factor

The projective plane crossing number ofC3 ×Cn

1993 ◽  
Vol 17 (6) ◽  
pp. 683-693
Author(s):  
Adrian Riskin
Keyword(s):  
Projective Plane ◽  
Crossing Number

scholarly journals Face morphology of brazilian and peruvian populations: analysis of proportion and linear measurement indexes

2017 ◽  
Vol 20 (3) ◽  
Author(s):  
Elaine Cristina Sousa Dos Santos ◽  
Diego Jesus Bradariz Pimentel ◽  
Laís Lopes Machado De Matos ◽  
Laís Valencise Magri ◽  
Ana Maria Bettoni Rodrigues Da Silva ◽  
...  
Keyword(s):  
Latin American ◽  
Linear Measurement ◽  
Linear Measurements ◽  
3D Images ◽  
Brazilian Sample ◽  
Face Width ◽  
The Face ◽  
Mouth Width ◽  
3D Stereophotogrammetry ◽  
Face Morphology

<p><strong>Objective: </strong>To compare the proportion and linear measurement indexes between Brazilian and Peruvian population through 3D stereophotogrammetry and to stablish the face profile of these two Latin American populations. <strong>Material and Methods: </strong>40 volunteers (Brazilian n=21– 10 males and 11 females; Peruvian n=19 – 8 males and 11 females) aged between 18 and 40 years (mean of 28.7±9.1) had landmarks marked on the face. Then, 3D images were obtained (VECTRA M3) and the indexes of proportion and linear measurement (face, nose, and lips) were calculated. The data were statistically analyzed by One-Way ANOVA (p&lt;0.05). <strong>Results: </strong>The proportion indexes did not reveal marked differences either between the studied populations or genders (p&gt;0.05). The following linear measurements showed intergroup statistically significant differences: face width and height, nose width and height, upper facial height, mouth width, protrusion of the nose tip (p&lt;0.05). The Brazilian females showed the smallest significant differences. <strong>Conclusions: </strong>Despite the different ethnic compositions, the Brazilian and Peruvian populations did not differ regarding the proportions of the face, nose, and lips. The differences observed in Brazilian females may be related to gender and/or to the Caucasian heritage of the Brazilian sample.</p><p><strong>Keywords</strong></p><p>Photogrammetry; Face; Tridimensional Image.<strong></strong></p>

scholarly journals Randomized heuristic for the maximum clique problem

2020 ◽  
Author(s):  
Shalin Shah
Keyword(s):  
Approximation Algorithm ◽  
Randomized Algorithm ◽  
Maximum Clique ◽  
Constant Factor ◽  
Maximum Clique Problem ◽  
Hard Problem ◽  
Np Hard ◽  
Np Hard Problem ◽  
Java Code ◽  
Clique Problem

<p>A clique in a graph is a set of vertices that are all directly connected</p><p>to each other i.e. a complete sub-graph. A clique of the largest size is</p><p>called a maximum clique. Finding the maximum clique in a graph is an</p><p>NP-hard problem and it cannot be solved by an approximation algorithm</p><p>that returns a solution within a constant factor of the optimum. In this</p><p>work, we present a simple and very fast randomized algorithm for the</p><p>maximum clique problem. We also provide Java code of the algorithm</p><p>in our git repository. Results show that the algorithm is able to find</p><p>reasonably good solutions to some randomly chosen DIMACS benchmark</p><p>graphs. Rather than aiming for optimality, we aim to find good solutions</p><p>very fast.</p>

scholarly journals Randomized heuristic for the maximum clique problem

2020 ◽  
Author(s):  
Shalin Shah
Keyword(s):  
Approximation Algorithm ◽  
Randomized Algorithm ◽  
Maximum Clique ◽  
Constant Factor ◽  
Maximum Clique Problem ◽  
Hard Problem ◽  
Np Hard ◽  
Np Hard Problem ◽  
Java Code ◽  
Clique Problem

<p>A clique in a graph is a set of vertices that are all directly connected</p><p>to each other i.e. a complete sub-graph. A clique of the largest size is</p><p>called a maximum clique. Finding the maximum clique in a graph is an</p><p>NP-hard problem and it cannot be solved by an approximation algorithm</p><p>that returns a solution within a constant factor of the optimum. In this</p><p>work, we present a simple and very fast randomized algorithm for the</p><p>maximum clique problem. We also provide Java code of the algorithm</p><p>in our git repository. Results show that the algorithm is able to find</p><p>reasonably good solutions to some randomly chosen DIMACS benchmark</p><p>graphs. Rather than aiming for optimality, we aim to find good solutions</p><p>very fast.</p>

Sign in / Sign up

Export Citation Format

Share Document