748 research outputs found
Weighted skeletons and fixed-share decomposition
AbstractWe introduce the concept of weighted skeleton of a polygon and present various decomposition and optimality results for this skeletal structure when the underlying polygon is convex
Voronoi Diagrams for Parallel Halflines and Line Segments in Space
We consider the Euclidean Voronoi diagram for a set of parallel halflines in 3-space.
A relation of this diagram to planar power diagrams is shown, and is used to
analyze its geometric and topological properties. Moreover, an easy-to-implement
space sweep algorithm is proposed that computes the Voronoi diagram for parallel halflines
at logarithmic cost per face. Previously only an approximation algorithm for this problem was known.
Our method of construction generalizes to Voronoi diagrams for parallel line segments,
and to higher dimensions
Max Dvořák and the History of Medieval Art
The intellectual development of Max Dvořák (1874-1921), one of the protagonists of the ‘Vienna School of Art History’, was characterized by a constant process of methodological self-criticism. His changing views on Medieval Art are known above all by two texts: The Enigma of the Art of the Van Eyck Brothers (1904), strongly influenced by Wickhoff and Riegl and by an ‘impressionistic’ view of modernity, and Idealism and Naturalism in Gothic Sculpture and Painting (1918), an essay dating to Dvořák’s late, ‘expressionistic’, period. Knowing only these two texts, the decisive turn undertaken by Dvořák around 1920 could be interpreted as a sudden change of paradigm. As the paper wants to show, this view has to be revised after having read and analyzed Dvořák’s hitherto unpublished university lectures on Western European Art in the Middle Ages which were given four times from 1906 to 1918
On k-Convex Polygons
We introduce a notion of -convexity and explore polygons in the plane that
have this property. Polygons which are \mbox{-convex} can be triangulated
with fast yet simple algorithms. However, recognizing them in general is a
3SUM-hard problem. We give a characterization of \mbox{-convex} polygons, a
particularly interesting class, and show how to recognize them in \mbox{} time. A description of their shape is given as well, which leads to
Erd\H{o}s-Szekeres type results regarding subconfigurations of their vertex
sets. Finally, we introduce the concept of generalized geometric permutations,
and show that their number can be exponential in the number of
\mbox{-convex} objects considered.Comment: 23 pages, 19 figure
Piecewise-Linear Farthest-Site Voronoi Diagrams
Voronoi diagrams induced by distance functions whose unit balls are convex polyhedra are piecewise-linear structures. Nevertheless, analyzing their combinatorial and algorithmic properties in dimensions three and higher is an intriguing problem. The situation turns easier when the farthest-site variants of such Voronoi diagrams are considered, where each site gets assigned the region of all points in space farthest from (rather than closest to) it.
We give asymptotically tight upper and lower worst-case bounds on the combinatorial size of farthest-site Voronoi diagrams for convex polyhedral distance functions in general dimensions, and propose an optimal construction algorithm. Our approach is uniform in the sense that (1) it can be extended from point sites to sites that are convex polyhedra, (2) it covers the case where the distance function is additively and/or multiplicatively weighted, and (3) it allows an anisotropic scenario where each site gets allotted its particular convex distance polytope
Partially Walking a Polygon
Deciding two-guard walkability of an n-sided polygon is a well-understood problem. We study the following more general question: How far can two guards reach from a given source vertex while staying mutually visible, in the (more realistic) case that the polygon is not entirely walkable? There can be Theta(n) such maximal walks, and we show how to find all of them in O(n log n) time
The Random Bit Complexity of Mobile Robots Scattering
We consider the problem of scattering robots in a two dimensional
continuous space. As this problem is impossible to solve in a deterministic
manner, all solutions must be probabilistic. We investigate the amount of
randomness (that is, the number of random bits used by the robots) that is
required to achieve scattering. We first prove that random bits are
necessary to scatter robots in any setting. Also, we give a sufficient
condition for a scattering algorithm to be random bit optimal. As it turns out
that previous solutions for scattering satisfy our condition, they are hence
proved random bit optimal for the scattering problem. Then, we investigate the
time complexity of scattering when strong multiplicity detection is not
available. We prove that such algorithms cannot converge in constant time in
the general case and in rounds for random bits optimal
scattering algorithms. However, we present a family of scattering algorithms
that converge as fast as needed without using multiplicity detection. Also, we
put forward a specific protocol of this family that is random bit optimal ( random bits are used) and time optimal ( rounds are used).
This improves the time complexity of previous results in the same setting by a
factor. Aside from characterizing the random bit complexity of mobile
robot scattering, our study also closes its time complexity gap with and
without strong multiplicity detection (that is, time complexity is only
achievable when strong multiplicity detection is available, and it is possible
to approach it as needed otherwise)
The lattice dimension of a graph
We describe a polynomial time algorithm for, given an undirected graph G,
finding the minimum dimension d such that G may be isometrically embedded into
the d-dimensional integer lattice Z^d.Comment: 6 pages, 3 figure
Optimizing the Access to Healthcare Services in Dense Refugee Hosting Urban Areas: A Case for Istanbul
With over 3.5 million refugees, Turkey continues to host the world's largest
refugee population. This introduced several challenges in many areas including
access to healthcare system. Refugees have legal rights to free healthcare
services in Turkey's public hospitals. With the aim of increasing healthcare
access for refugees, we looked at where the lack of infrastructure is felt the
most. Our study attempts to address these problems by assessing whether Migrant
Health Centers' locations are optimal. The aim of this study is to improve
refugees' access to healthcare services in Istanbul by improving the locations
of health facilities available to them. We used call data records provided by
Turk Telekom.Comment: version to submit for D4R competitio
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