Deterministic Construction of Regular Geometric Graphs with Short Average Distance and Limited Edge Length

2016 ◽  
pp. 295-309
Author(s):  
Satoshi Fujita ◽  
Koji Nakano ◽  
Michihiro Koibuchi ◽  
Ikki Fujiwara
Keyword(s):  
Average Distance ◽  
Edge Length ◽  
Geometric Graphs ◽  
Deterministic Construction

scholarly journals Approximating the Edge Length of 2-Edge Connected Planar Geometric Graphs on a Set of Points

2012 ◽  
pp. 255-266 ◽  
Author(s):  
Stefan Dobrev ◽  
Evangelos Kranakis ◽  
Danny Krizanc ◽  
Oscar Morales-Ponce ◽  
Ladislav Stacho
Keyword(s):  
Edge Length ◽  
Geometric Graphs ◽  
Set Of Points

DISTANCE PRESERVING SUBTREES IN MINIMUM AVERAGE DISTANCE SPANNING TREES

2013 ◽  
Vol 05 (03) ◽  
pp. 1350010
Author(s):  
LAURENT LYAUDET ◽  
PAULIN MELATAGIA YONTA ◽  
MAURICE TCHUENTE ◽  
RENÉ NDOUNDAM
Keyword(s):  
Approximate Solution ◽  
Spanning Tree ◽  
Path Length ◽  
Spanning Trees ◽  
Undirected Graph ◽  
Average Distance ◽  
Edge Length ◽  
The Other ◽  
First Results ◽  
Positive Length

Given an undirected graph G = (V, E) with n vertices and a positive length w(e) on each edge e ∈ E, we consider Minimum Average Distance (MAD) spanning trees i.e., trees that minimize the path length summed over all pairs of vertices. One of the first results on this problem is due to Wong who showed in 1980 that a Distance Preserving (DP) spanning tree rooted at the median of G is a 2-approximate solution. On the other hand, Dankelmann has exhibited in 2000 a class of graphs where no MAD spanning tree is distance preserving from a vertex. We establish here a new relation between MAD and DP trees in the particular case where the lengths are integers. We show that in a MAD spanning tree of G, each subtree H′ = (V′, E′) consisting of a vertex [Formula: see text] and the union of branches of [Formula: see text] that are each of size less than or equal to [Formula: see text], where w+ is the maximum edge-length in G, is a distance preserving spanning tree of the subgraph of G induced by V′.

scholarly journals Almost sure central limit theorems in stochastic geometry

2020 ◽  
Vol 52 (3) ◽  
pp. 705-734
Author(s):  
Giovanni Luca Torrisi ◽  
Emilio Leonardi
Keyword(s):  
Central Limit ◽  
Stochastic Geometry ◽  
Limit Theorems ◽  
Voronoi Tessellation ◽  
Edge Length ◽  
Central Limit Theorems ◽  
Geometric Graphs ◽  
Random Geometric Graphs ◽  
Poisson Space ◽  
Set Approximation

AbstractWe prove an almost sure central limit theorem on the Poisson space, which is perfectly tailored for stabilizing functionals arising in stochastic geometry. As a consequence, we provide almost sure central limit theorems for (i) the total edge length of the k-nearest neighbors random graph, (ii) the clique count in random geometric graphs, and (iii) the volume of the set approximation via the Poisson–Voronoi tessellation.

On the Location of Quiescent Prominences with Respect to Coronal Holes

1979 ◽  
Vol 44 ◽  
pp. 209-213
Author(s):  
B. Rompolt
Keyword(s):  
Coronal Hole ◽  
Average Distance ◽  
Coronal Holes

The aim of this contribution is to turn attention to a peculiarity of location of the filaments (quiescent prominences) with respect to the boundaries of the coronal holes. It is generally known that quiescent prominences are located at some distance from the boundary of coronal holes. My intention was to check whether the average distance between the nearest border of a coronal hole and the prominence is comparable to the average horizontal extension of a helmet structure overlying the prominence. As well as, whether this average distance depends upon the orientation of the long axis of the prominence with respect to the nearest boundary of the coronal hole.

Mobile network synthesis strategy

2019 ◽  
pp. 98-101
Author(s):  
V. Lyandres
Keyword(s):  
Average Distance ◽  
Mobile Network ◽  
Base Station ◽  
Service Area ◽  
Base Stations ◽  
Frequency Assignment ◽  
Network Synthesis ◽  
Universal Method ◽  
Synthesis Strategy ◽  
Adaptive Vector Quantization

Introduction:Effective synthesis of а mobile communication network includes joint optimisation of two processes: placement of base stations and frequency assignment. In real environments, the well-known cellular concept fails due to some reasons, such as not homogeneous traffic and non-isotropic wave propagation in the service area.Purpose:Looking for the universal method of finding a network structure close to the optimal.Results:The proposed approach is based on the idea of adaptive vector quantization of the network service area. As a result, it is reduced to a 2D discrete map split into zones with approximately equal number of service requests. In each zone, the algorithm finds such coordinates of its base station that provide the shortest average distance to all subscribers. This method takes into account the shortage of the a priory information about the current traffic, ensures maximum coverage of the service area, and what is not less important, significantly simplifies the process of frequency assignment.

What Makes a City Bikeable? A Study of Intercity and Intracity Patterns of Bicycle Ridership using Mobike Big Data Records

2020 ◽  
Vol 46 (1) ◽  
pp. 55-75
Author(s):  
Ying Long ◽  
Jianting Zhao
Keyword(s):  
Big Data ◽  
Average Distance ◽  
Policy Implications ◽  
Rating System ◽  
City Centre ◽  
Average Score ◽  
Policy Makers ◽  
Usage Frequency ◽  
Share Data ◽  
The City

This paper examines how mass ridership data can help describe cities from the bikers' perspective. We explore the possibility of using the data to reveal general bikeability patterns in 202 major Chinese cities. This process is conducted by constructing a bikeability rating system, the Mobike Riding Index (MRI), to measure bikeability in terms of usage frequency and the built environment. We first investigated mass ridership data and relevant supporting data; we then established the MRI framework and calculated MRI scores accordingly. This study finds that people tend to ride shared bikes at speeds close to 10 km/h for an average distance of 2 km roughly three times a day. The MRI results show that at the street level, the weekday and weekend MRI distributions are analogous, with an average score of 49.8 (range 0–100). At the township level, high-scoring townships are those close to the city centre; at the city level, the MRI is unevenly distributed, with high-MRI cities along the southern coastline or in the middle inland area. These patterns have policy implications for urban planners and policy-makers. This is the first and largest-scale study to incorporate mobile bike-share data into bikeability measurements, thus laying the groundwork for further research.

Approach to spatial modeling of networks and groups of objects on the basis of the weighted graph construction procedure

2020 ◽  
Vol 964 (10) ◽  
pp. 49-58
Author(s):  
V.I. Bilan ◽  
A.N. Grigor’ev ◽  
G.G. Dmitrikov ◽  
E.A. Dudin
Keyword(s):  
Spatial Configuration ◽  
Weighted Graph ◽  
Edge Length ◽  
Buffer Zones ◽  
Typical Structure ◽  
Spatial Graph ◽  
Object Based ◽  
Complementary Graph ◽  
Spatial Parameters ◽  
The Given

The direction of research on the development of a scientific and methodological tool for the analysis of spatial objects in order to determine their generalized spatial parameters was selected. An approach to the problem of modeling networks and groups of objects based on the synthesis of a weighted graph is proposed. The spatial configuration of objects based on the given conditions is described by a weighted graph, the edge length of which is considered as the weight of the edges. A generalization to the typical structure of a spatial graph is formulated; its essence is representation of nodal elements as two-dimensional (polygonal) objects. To take into account the restrictions on the convergence of the vertices described by the buffer zones, a complementary graph is formed. An algorithm for constructing the implementation of a spatial object based on the sequential determination of vertices that comply with the given conditions is proposed. Using the software implementation of the developed algorithm, an experiment was performed to evaluate the spatial parameters of the simulated objects described by typical graph structures. The following parameters were investigated as spatial ones

Temporal Changes in Habitat Selection and Nest Spacing in a Colony of Ross' and Lesser Snow Geese

The Auk ◽  
1983 ◽  
Vol 100 (2) ◽  
pp. 335-343 ◽  
Author(s):  
M. Robert McLandress
Keyword(s):  
Nearest Neighbor ◽  
Average Distance ◽  
Habitat Preferences ◽  
Nearest Neighbors ◽  
Nest Density ◽  
Snow Goose ◽  
Snow Geese ◽  
Lesser Snow Geese ◽  
Average Size ◽  
Island Habitats

Abstract I studied the nesting colony of Ross' Geese (Chen rossii) and Lesser Snow Geese (C. caerulescens caerulescens) at Karrak Lake in the central Arctic of Canada in the summer of 1976. Related studies indicated that this colony had grown from 18,000 birds in 1966-1968 to 54,500 birds in 1976. In 1976, geese nested on islands that were used in the late 1960's and on an island and mainland sites that were previously unoccupied. Average nest density in 1976 was three-fold greater than in the late 1960's. Consequently, the average distance to nearest neighbors of Ross' Geese in 1976 was half the average distance determined 10 yr earlier. The mean clutch size of Ross' Geese was greater in island habitats where nest densities were high than in less populated island or mainland habitats. The average size of Snow Goose clutches did not differ significantly among island habitats but was larger at island than at mainland sites. Large clutches were most likely attributable to older and/or earlier nesting females. Habitat preferences apparently differed between species. Small clutches presumably indicated that young geese nested in areas where nest densities were low. The establishment of mainland nesting at Karrak Lake probably began with young Snow Geese using peripheral areas of the colony. Young Ross' Geese nested in sparsely populated habitats on islands to a greater extent than did Snow Geese. Ross' Geese also nested on the mainland but in lower densities than Ross' Geese nesting in similar island habitats. Successful nests with the larger clutches had closer conspecific neighbors than did successful nests with smaller clutches. The species composition of nearest neighbors changed significantly with distance from Snow Goose nests but not Ross' Goose nests. Nesting success was not affected by the species of nearest neighbor, however. Because they have complementary antipredator adaptations, Ross' and Snow geese may benefit by nesting together.

scholarly journals Normalized Sombor Indices as Complexity Measures of Random Networks

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 976
Author(s):  
R. Aguilar-Sánchez ◽  
J. Méndez-Bermúdez ◽  
José Rodríguez ◽  
José Sigarreta
Keyword(s):  
Random Matrix ◽  
Adjacency Matrix ◽  
Matrix Theory ◽  
Computational Study ◽  
Random Networks ◽  
Geometric Graphs ◽  
Theory Approach ◽  
Complexity Measures ◽  
Random Geometric Graphs ◽  
Highly Correlated

We perform a detailed computational study of the recently introduced Sombor indices on random networks. Specifically, we apply Sombor indices on three models of random networks: Erdös-Rényi networks, random geometric graphs, and bipartite random networks. Within a statistical random matrix theory approach, we show that the average values of Sombor indices, normalized to the order of the network, scale with the average degree. Moreover, we discuss the application of average Sombor indices as complexity measures of random networks and, as a consequence, we show that selected normalized Sombor indices are highly correlated with the Shannon entropy of the eigenvectors of the adjacency matrix.

scholarly journals Geometric graphs from data to aid classification tasks with Graph Convolutional Networks

Patterns ◽  
2021 ◽  
Vol 2 (4) ◽  
pp. 100237
Author(s):  
Yifan Qian ◽  
Paul Expert ◽  
Pietro Panzarasa ◽  
Mauricio Barahona
Keyword(s):  
Geometric Graphs ◽  
Convolutional Networks ◽  
Classification Tasks
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