3,198 research outputs found
Random planar graphs and the London street network
In this paper we analyse the street network of London both in its primary and
dual representation. To understand its properties, we consider three idealised
models based on a grid, a static random planar graph and a growing random
planar graph. Comparing the models and the street network, we find that the
streets of London form a self-organising system whose growth is characterised
by a strict interaction between the metrical and informational space. In
particular, a principle of least effort appears to create a balance between the
physical and the mental effort required to navigate the city
L-Drawings of Directed Graphs
We introduce L-drawings, a novel paradigm for representing directed graphs
aiming at combining the readability features of orthogonal drawings with the
expressive power of matrix representations. In an L-drawing, vertices have
exclusive - and -coordinates and edges consist of two segments, one
exiting the source vertically and one entering the destination horizontally.
We study the problem of computing L-drawings using minimum ink. We prove its
NP-completeness and provide a heuristics based on a polynomial-time algorithm
that adds a vertex to a drawing using the minimum additional ink. We performed
an experimental analysis of the heuristics which confirms its effectiveness.Comment: 11 pages, 7 figure
Parallelization of cycle-based logic simulation
Verification of digital circuits by Cycle-based simulation can be performed in parallel. The parallel implementation requires two phases: the compilation phase, that sets up the data needed for the
execution of the simulation, and the simulation phase, that consists in executing the parallel simulation of the considered circuit for a certain number of cycles. During the early phase of design, compilation phase has to be repeated each time a bug is found. Thus, if the time of the compilation phase is too high, the advantages stemming from the parallel approach may be lost. In this work we propose an
effective version of the compilation phase and compute the corresponding execution time. We also analyze the percentage of execution time required by the different steps of the compilation phase for
a set of literature benchmarks. Further, we implemented the simulation phase exploiting the GPU architecture, and we computed the execution times for a set of benchmarks obtaining values comparable
with literature ones. Finally, we implemented the sequential version of the Cycle-based simulation in such a way that the execution time is optimized. We used the sequential values to compute the speedup
of the parallel version for the considered set of benchmarks
Searching edges in the overlap of two plane graphs
Consider a pair of plane straight-line graphs, whose edges are colored red
and blue, respectively, and let n be the total complexity of both graphs. We
present a O(n log n)-time O(n)-space technique to preprocess such pair of
graphs, that enables efficient searches among the red-blue intersections along
edges of one of the graphs. Our technique has a number of applications to
geometric problems. This includes: (1) a solution to the batched red-blue
search problem [Dehne et al. 2006] in O(n log n) queries to the oracle; (2) an
algorithm to compute the maximum vertical distance between a pair of 3D
polyhedral terrains one of which is convex in O(n log n) time, where n is the
total complexity of both terrains; (3) an algorithm to construct the Hausdorff
Voronoi diagram of a family of point clusters in the plane in O((n+m) log^3 n)
time and O(n+m) space, where n is the total number of points in all clusters
and m is the number of crossings between all clusters; (4) an algorithm to
construct the farthest-color Voronoi diagram of the corners of n axis-aligned
rectangles in O(n log^2 n) time; (5) an algorithm to solve the stabbing circle
problem for n parallel line segments in the plane in optimal O(n log n) time.
All these results are new or improve on the best known algorithms.Comment: 22 pages, 6 figure
Decoding the urban grid: or why cities are neither trees nor perfect grids
In a previous paper (Figueiredo and Amorim, 2005), we introduced the continuity
lines, a compressed description that encapsulates topological and geometrical
properties of urban grids. In this paper, we applied this technique to a large
database of maps that included cities of 22 countries. We explore how this
representation encodes into networks universal features of urban grids and, at the
same time, retrieves differences that reflect classes of cities. Then, we propose an
emergent taxonomy for urban grids
Random planar graphs and the London street network
In this paper we analyse the street network of London both in its primary and dual representation. To understand its properties, we consider three idealised models based on a grid, a static random planar graph and a growing random planar graph. Comparing the models and the street network, we find that the streets of London form a self-organising system whose growth is characterised by a strict interaction between the metrical and informational space. In particular, a principle of least effort appears to create a balance between the physical and the mental effort required to navigate the city
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