On the dimension to represent a graph by a unit distance graph

1990 ◽  
Vol 6 (4) ◽  
pp. 365-367 ◽  
Author(s):  
Hiroshi Maehara ◽  
Vojtech Rödl
Keyword(s):  
Distance Graph ◽  
Unit Distance ◽  
Unit Distance Graph

scholarly journals Monochromatic equilateral triangles in the unit distance graph

2020 ◽  
Vol 52 (4) ◽  
pp. 687-692
Author(s):  
Eric Naslund
Keyword(s):  
Distance Graph ◽  
Unit Distance ◽  
Unit Distance Graph ◽  
Equilateral Triangles

scholarly journals Distances in a rigid unit-distance graph in the plane

1991 ◽  
Vol 31 (2) ◽  
pp. 193-200 ◽  
Author(s):  
Hiroshi Maehara
Keyword(s):  
Distance Graph ◽  
Unit Distance ◽  
Unit Distance Graph

scholarly journals Distributed Dynamic Storage in Wireless Networks

2005 ◽  
Vol 1 (3-4) ◽  
pp. 355-371 ◽  
Author(s):  
Constantinos Georgiou ◽  
Evangelos Kranakis ◽  
Ricardo Marceí-n-Jiménez ◽  
Sergio Rajsbaum ◽  
Jorge Urrutia
Keyword(s):  
Spanning Trees ◽  
Distributed Storage ◽  
Network Size ◽  
Distance Graph ◽  
Unit Distance ◽  
Network Algorithms ◽  
Empty Intersection ◽  
Unit Distance Graph ◽  
Distributed Solutions ◽  
The Difference

This paper assumes a set of identical wireless hosts, each one aware of its location. The network is described by a unit distance graph whose vertices are points on the plane two of which are connected if their distance is at most one. The goal of this paper is to design local distributed solutions that require a constant number of communication rounds, independently of the network size or diameter. This is achieved through a combination of distributed computing and computational complexity tools. Starting with a unit distance graph, the paper shows: 1. How to extract a triangulated planar spanner; 2. Several algorithms are proposed to construct spanning trees of the triangulation. Also, it is described how to construct three spanning trees of the Delaunay triangulation having pairwise empty intersection, with high probability. These algorithms are interesting in their own right, since trees are a popular structure used by many network algorithms; 3. A load balanced distributed storage strategy on top of the trees is presented, that spreads replicas of data stored in the hosts in a way that the difference between the number of replicas stored by any two hosts is small. Each of the algorithms presented is local, and hence so is the final distributed storage solution, obtained by composing all of them. This implies that the solution adapts very quickly, in constant time, to network topology changes. We present a thorough experimental evaluation of each of the algorithms supporting our claims.

103.27 A property of a particular unit-distance graph

2019 ◽  
Vol 103 (557) ◽  
pp. 353-356
Author(s):  
Martin Griffiths
Keyword(s):  
Distance Graph ◽  
Unit Distance ◽  
Unit Distance Graph

scholarly journals Subdividing a Graph Toward a Unit-distance Graph in the Plane

2000 ◽  
Vol 21 (2) ◽  
pp. 223-229 ◽  
Author(s):  
Severino V. Gervacio ◽  
Hiroshi Maehara
Keyword(s):  
Distance Graph ◽  
Unit Distance ◽  
Unit Distance Graph

scholarly journals Unit Distance Graphs and Algebraic Integers

2019 ◽  
Author(s):  
Danylo Radchenko
Keyword(s):  
Algebraic Integers ◽  
Unit Distance ◽  
Distance Graphs

scholarly journals Electric Vehicle Integration into Road Transportation, Intelligent Transportation, and Electric Power Systems: An Abu Dhabi Case Study

Smart Cities ◽  
2021 ◽  
Vol 4 (3) ◽  
pp. 1039-1057
Author(s):  
Amro M. Farid ◽  
Asha Viswanath ◽  
Reem Al-Junaibi ◽  
Deema Allan ◽  
Thomas J. T. Van der Van der Wardt
Keyword(s):  
Electric Power ◽  
Intelligent Transportation ◽  
Energy System ◽  
Transportation System ◽  
Electric Power System ◽  
Abu Dhabi ◽  
Road Transportation ◽  
Unit Distance ◽  
The Impact

Recently, electric vehicles (EV) have gained much attention as a potential enabling technology to support CO2 emissions reduction targets. Relative to their internal combustion vehicle counterparts, EVs consume less energy per unit distance, and add the benefit of not emitting any carbon dioxide in operation and instead shift their emissions to the existing local fleet of power generation. However, the true success of EVs depends on their successful integration with the supporting infrastructure systems. Building upon the recently published methodology for the same purpose, this paper presents a “systems-of-systems” case study assessing the impacts of EVs on these three systems in the context of Abu Dhabi. For the physical transportation system, a microscopic discrete-time traffic operations simulator is used to predict the kinematic state of the EV fleet over the duration of one day. For the impact on the intelligent transportation system (ITS), the integration of EVs into Abu Dhabi is studied using a multi-domain matrix (MDM) of the Abu Dhabi Department of Transportation ITS. Finally, for the impact on the electric power system, the EV traffic flow patterns from the CMS are used to calculate the timing and magnitude of charging loads. The paper concludes with the need for an intelligent transportation-energy system (ITES) which would coordinate traffic and energy management functionality.

New upper bound for the chromatic number of a random subgraph of a distance graph

2015 ◽  
Vol 97 (3-4) ◽  
pp. 326-332 ◽  
Author(s):  
A. S. Gusev
Keyword(s):  
Chromatic Number ◽  
Upper Bound ◽  
Distance Graph ◽  
Random Subgraph

Evaluating the Safety of Shared-Use Paths

2005 ◽  
Vol 1939 (1) ◽  
pp. 99-106 ◽  
Author(s):  
Lisa Aultman-Hall ◽  
Jeffrey LaMondia
Keyword(s):  
Sample Size ◽  
Event Rate ◽  
The Self ◽  
Travel Patterns ◽  
Unit Distance ◽  
Safety Concerns ◽  
Crash Rates ◽  
Incident Rate

The project described in this paper involved the design of a survey of shared-use path safety for use at three facilities in Connecticut in the fall of 2002 and the summer of 2003. The objective was to collect self-reported information on collision and fall events and on travel exposure so that crash rates could be developed. The analysis of the self-reported events and travel patterns provides complementary data that are not available from other sources but are needed to address safety concerns on these facilities. The strengths of this approach include the collection of underreported minor events and the ability to estimate travel exposure and thus allow the estimation of crash rates per unit distance. The sample size of 684 was sufficient only for the development of aggregate crash rates, which suggest that skaters have the highest rates, followed by bicyclists and then pedestrians. The bicycle event rate was three times that of pedestrians, while the rate for skaters was more than six times that for pedestrians. Falls were more frequently reported than collisions, and they were more often associated with an injury. The overall incident rate for each of the three individual facilities was the highest for the path with the highest user volume and highest percentage of skaters and cyclists.

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