Hardness results for computing optimal locally Gabriel graphs

Delaunay and Gabriel graphs are widely studied geo-metric proximity structures. Motivated by applications in wireless routing, relaxed versions of these graphs known as Locally Delaunay Graphs (LDGs) and Lo-cally Gabriel Graphs (LGGs) have been proposed. We propose another generalization of LGGs called Gener-alized Locally Gabriel Graphs (GLGGs) in the context when certain edges are forbidden in the graph. Unlike a Gabriel Graph, there is no unique LGG or GLGG for a given point set because no edge is necessarily in-cluded or excluded. This property allows us to choose an LGG/GLGG that optimizes a parameter of interest in the graph. We show that computing an edge max-imum GLGG for a given problem instance is NP-hard and also APX-hard. We also show that computing an LGG on a given point set with dilation ≤k is NP-hard. Finally, we give an algorithm to verify whether a given geometric graph G= (V, E) is a valid LGG.

On Locally Gabriel Geometric Graphs

Let be a set of points in the plane. A geometric graph on is said to be locally Gabriel if for every edge in , the Euclidean disk with the segment joining and as diameter does not contain any points of that are neighbors of or in . A locally Gabriel graph(LGG) is a generalization of Gabriel graph and is motivated by applications in wireless networks. Unlike a Gabriel graph, there is no unique LGG on a given point set since no edge in a LGG is necessarily included or excluded. Thus the edge set of the graph can be customized to optimize certain network parameters depending on the application. The unit distance graph(UDG), introduced by Erdos, is also a LGG. In this paper, we show the following combinatorial bounds on edge complexity and independent sets of LGG: (i) For any , there exists LGG with edges. This improves upon the previous best bound of . (ii) For various subclasses of convex point sets, we show tight linear bounds on the maximum edge complexity of LGG. (iii) For any LGG on any point set, there exists an independent set of size .

Amor, muerte y esperanza : reflexiones desde Gabriel Marcel

Resumen: No vivimos solos ni morimos solos. Por ello el acompañamiento del enfermo terminal desde una actitud de amor, sostenido en su base por la esperanza trascendente, es ciertamente necesario como actitud cristiana de donación, y su reflexión se incorpora a toda antropología que no deje de lado la tanatología. Si la antropología margina el “thanatos”, se torna fragmentaria e incompleta. Morir no es el fin de la biografía que le “pasa” a los demás: es la experiencia universal a la cual cada uno ha de prepararse. Este asunto será analizado teniendo como guía a un destacado filósofo francés, Gabriel Marcel, quien, de algún modo, ha dado luz con sus escritos y su preocupación vital sobre esta temática.

[Discurso do Deputado Hermes Gabriel : Sessão da Câmara dos Deputados de 02 de maio de 1960]

Discurso proferido durante a 1ª Sessão da Câmara dos Deputados na nova capital do país. Questão de ordem sobre as irradiações das sessões da Câmara e a respeito da distribuição do Diário do Congresso Nacional - DCN.

La traducción vista desde la perspectiva del concepto de "literatura universal" de Johann Wolfgang von Goethe (1749-1832)

Eguíluz, Federico; Merino, Raquel; Olsen, Vickie; Pajares, Eterio; Santamaría, José Miguel (eds.)

Cartas enviadas por Gabriel Aresti a Justo Garate entre 1960 y 1968

1 nota y 3 cartas (manuscritas) ; entre 155x047mm y 210x295mm. Caja 1 - Carpeta 47

Structural geology of the region between Pacoima and Little Tujunga Canyons, San Gabriel Mountains, California

An area of about 25 square miles in the western part of the San Gabriel Mountains was mapped on a scale of 1000 feet to the inch. Special attention was given to the structural geology, particularly the relations between the different systems of faults, of which the San Gabriel fault system and the Sierra Madre fault system are the most important ones. The present distribution and relations of the rocks suggests that the southern block has tilted northward against a more stable mass of old rocks which was raised up during a Pliocene or post-Pliocene orogeny. It is suggested that this northward tilting of the block resulted in the group of thrust faults which comprise the Sierra Madre fault system. It is show that this hypothesis fits the present distribution of the rocks and occupies a logical place in the geologic history of the region as well or better than any other hypothesis previously offered to explain the geology of the region.

San Gabriel Valley sewerage system

The disposal of sewage is the most important item in public sanitation. It is the most important present day problem in every city whether large or small. The direct cause of the majority of epidemics is the contamination of the water supply of the city by the excreta of man or animal. Public health varies directly as public sanitation, and if the public sanitation be good, the liability of sickness caused by contamination of the water supply is greatly lessened. When a city outgrows its sewerage system the public health becomes endangered. There are two causes for the increased amount of sewerage, increase in population and increase in industrial and manufacturing wastes. The main problem in this connection is the ultimate disposal of the matter which reaches the sewers.

Harritik herrira. Gabriel Arestiren paperak euskal kultura eta gizartean, 1954-2014

390 p.

Copia del nombramiento de Gabriel Arana Basabe como Comandante Jefe del Batallón Munguía, del Euzko-Gudarostea del PNV

Fecha: 16 de noviembre de 1936 / Unidad de ínstalación: Carpeta Rectorado - C-1 / Nº de pág.: 1. Copia del original mecanografiado, con membrete y sello del Euzko Gudarostea y firma de Ramón de Azkue

O avesso da costura: uma análise dos escritos de Gabriel Soares de Sousa (c.1540-1591)

O colono português Gabriel Soares de Sousa apresentou à corte de Felipe II da Espanha, por volta de 1587, um dos mais importantes registros sobre o Brasil quinhentista, o Tratado descritivo do Brasil em 1587, e o bem menos conhecido Capítulos de Gabriel Soares de Sousa contra os padres da Companhia de Jesus no Brasil. Esta tese apresenta uma análise da história destes manuscritos quinhentistas, examinado como chegaram até os seus formatos atuais e as suas leituras através dos tempos.