Complexity results on the minimum width drawing problem for rooted unordered trees

Author(s):  
Kunihiko Hayashi ◽  
Sumio Masuda
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.


Author(s):  
Garrett Cullity

Three things often recognized as central to morality are concern for others’ welfare, respect for their self-expression, and cooperation in worthwhile collective activity. When philosophers have proposed theories of the substance of morality, they have typically looked to one of these three sources to provide a single, fundamental principle of morality—or they have tried to formulate a master-principle for morality that combines these three ideas in some way. This book views them instead as three independently important foundations of morality. It sets out a plural-foundation moral theory with affinities to that of W. D. Ross. There are major differences: the account of the foundations of morality differs from Ross’s, and there is a more elaborate explanation of how the rest of morality derives from them. However, the overall aim is similar. This is to illuminate the structure of morality by showing how its complex content is generated from a relatively simple set of underlying elements—the complexity results from the various ways in which one part of morality can derive from another, and the various ways in which the derived parts of morality can interact. Plural-foundation moral theories are sometimes criticized for having nothing helpful to say about cases in which their fundamental norms conflict. Responding to this, the book concludes with three detailed applications of the theory: to the questions surrounding paternalism, the use of others as means, and our moral responsibilities as consumers.


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.


1994 ◽  
Vol 25 (3) ◽  
pp. 122-123 ◽  
Author(s):  
Michael T. Hallett ◽  
H. Todd Wareham

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.


2016 ◽  
Vol 389 ◽  
pp. 237-252
Author(s):  
Farah Ben-Naoum ◽  
Christophe Godin
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.


2014 ◽  
Vol 663 ◽  
pp. 347-353
Author(s):  
Layth H. Jawad ◽  
Shahrir Abdullah ◽  
Zulkifli R. ◽  
Wan Mohd Faizal Wan Mahmood

A numerical study that was made in a three-dimensional flow, carried out in a modified centrifugal compressor, having vaned diffuser stage, used as an automotive turbo charger. In order to study the influence of vaned diffuser meridional outlet section with a different width ratio of the modified centrifugal compressor. Moreover, the performance of the centrifugal compressor was dependent on the proper matching between the compressor impeller along the vaned diffuser. The aerodynamic characteristics were compared under different meridional width ratio. In addition, the velocity vectors in diffuser flow passages, and the secondary flow in cross-section near the outlet of diffuser were analysed in detail under different meridional width ratio. Another aim of this research was to study and simulate the effect of vaned diffuser on the performance of a centrifugal compressor. The simulation was undertaken using commercial software so-called ANSYS CFX, to predict numerically the performance charachteristics. The results were generated from CFD and were analysed for better understanding of the fluid flow through centrifugal compressor stage and as a result of the minimum width ratio the flow in diffuser passage tends to be uniformity. Moreover, the backflow and vortex near the pressure surface disappear, and the vortex and detachment near the suction surface decrease. Conclusively, it was observed that the efficiency was increased and both the total pressure ratio and static pressure for minimum width ratio are increased.


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