scholarly journals Minimum-width grid drawings of plane graphs extend abstract

Author(s):  
Marek Chrobak ◽  
Shin-ichi Nakano
1998 ◽  
Vol 11 (1) ◽  
pp. 29-54 ◽  
Author(s):  
Marek Chrobak ◽  
Shin-ichi Nakano
Keyword(s):  

10.37236/1734 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
David Arthur

An arc-representation of a graph is a function mapping each vertex in the graph to an arc on the unit circle in such a way that adjacent vertices are mapped to intersecting arcs. The width of such a representation is the maximum number of arcs passing through a single point. The arc-width of a graph is defined to be the minimum width over all of its arc-representations. We extend the work of Barát and Hajnal on this subject and develop a generalization we call restricted arc-width. Our main results revolve around using this to bound arc-width from below and to examine the effect of several graph operations on arc-width. In particular, we completely describe the effect of disjoint unions and wedge sums while providing tight bounds on the effect of cones.


2021 ◽  
Vol 13 (8) ◽  
pp. 1525
Author(s):  
Gang Tang ◽  
Congqiang Tang ◽  
Hao Zhou ◽  
Christophe Claramunt ◽  
Shaoyang Men

Most Coverage Path Planning (CPP) strategies based on the minimum width of a concave polygonal area are very likely to generate non-optimal paths with many turns. This paper introduces a CPP method based on a Region Optimal Decomposition (ROD) that overcomes this limitation when applied to the path planning of an Unmanned Aerial Vehicle (UAV) in a port environment. The principle of the approach is to first apply a ROD to a Google Earth image of a port and combining the resulting sub-regions by an improved Depth-First-Search (DFS) algorithm. Finally, a genetic algorithm determines the traversal order of all sub-regions. The simulation experiments show that the combination of ROD and improved DFS algorithm can reduce the number of turns by 4.34%, increase the coverage rate by more than 10%, and shorten the non-working distance by about 29.91%. Overall, the whole approach provides a sound solution for the CPP and operations of UAVs in port environments.


Author(s):  
Nicholas A. Coppola ◽  
Wesley E. Marshall

Data on sidewalks have long been deficient. But advances in remote sensing are beginning to increase data prevalence and accuracy. These sidewalk datasets rarely, if ever, account for static obstructions in the sidewalk such as signs, street furniture, or trees. This paper seeks to determine how much of a difference accounting for static obstructions will make when measuring the clear width of sidewalks. We extracted the minimum width of sidewalk surfaces—both with and without accounting for static obstructions—for the entirety of Cambridge, MA, using new GIS methods described in this paper. We then compared these results against Americans with Disabilities Act (ADA) standards for clear width as well as national and federal sidewalk guidelines. The results suggest a significant decrease in the average clear width of sidewalks when accounting for static obstructions. More specifically, the clear width of the average sidewalk drops from 4.5 ft (1.4 m) to 3.5 ft (1.1 m). The percentage of sidewalk segments meeting the 3-ft ADA standard drops from 78% to 51% when accounting for static obstructions. For the proposed 4-ft (1.2-m) ADA standard, it plunges from 59% of sidewalk segments meeting the width threshold to 31%. These results demonstrate that not accounting for static obstructions could lead to a gross overestimation of seemingly adequate sidewalks and an unrealistic assessment of sidewalk infrastructure and pedestrian accessibility.


2021 ◽  
Vol 1897 (1) ◽  
pp. 012077
Author(s):  
Rawah A. Zaben ◽  
Israa M. Tawfik
Keyword(s):  

2021 ◽  
Vol 863 ◽  
pp. 40-52
Author(s):  
Giuseppe Liotta ◽  
Fabrizio Montecchiani ◽  
Alessandra Tappini

1986 ◽  
Vol 32 (13-16) ◽  
pp. 245-256 ◽  
Author(s):  
Armin Hemmerling
Keyword(s):  

1999 ◽  
Vol 76 (1) ◽  
pp. 117-126 ◽  
Author(s):  
Peter Che Bor Lam ◽  
Baogang Xu ◽  
Jiazhuang Liu
Keyword(s):  

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
A. R. Sufizadeh ◽  
S. A. A. Akbari Mousavi

Dissimilar electron beam welding of 316L austenitic stainless steel and AISI 4340 low alloy high strength steel has been studied. Studies are focused on effect of beam current on weld geometry, optical and scanning electron microscopy, X-ray diffraction of the weld microstructures, and heat affected zone. The results showed that the increase of beam current led to increasing depths and widths of the welds. The optimum beam current was 2.8 mA which shows full penetration with minimum width. The cooling rates were calculated for optimum sample by measuring secondary dendrite arm space and the results show that high cooling rates lead to austenitic microstructure. Moreover, the metallography result shows the columnar and equiaxed austenitic microstructures in weld zone. A comparison of HAZ widths depicts the wider HAZ in the 316L side. The tensile tests results showed that the optimum sample fractured from base metal in AISI 316L side with the UTS values is much greater than the other samples. Moreover, the fractography study presents the weld cross sections with dimples resembling ductile fracture. The hardness results showed that the increase of the beam current led to the formation of a wide softening zone as HAZ in AISI 4340 side.


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