454 research outputs found
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New Applications of the Nearest-Neighbor Chain Algorithm
The nearest-neighbor chain algorithm was proposed in the eighties as a way to speed up certain hierarchical clustering algorithms. In the first part of the dissertation, we show that its application is not limited to clustering. We apply it to a variety of geometric and combinatorial problems. In each case, we show that the nearest-neighbor chain algorithm finds the same solution as a preexistent greedy algorithm, but often with an improved runtime. We obtain speedups over greedy algorithms for Euclidean TSP, Steiner TSP in planar graphs, straight skeletons, a geometric coverage problem, and three stable matching models. In the second part, we study the stable-matching Voronoi diagram, a type of plane partition which combines properties of stable matchings and Voronoi diagrams. We propose political redistricting as an application. We also show that it is impossible to compute this diagram in an algebraic model of computation, and give three algorithmic approaches to overcome this obstacle. One of them is based on the nearest-neighbor chain algorithm, linking the two parts together
Approximation algorithms for multi-facility location
This thesis deals with the development and implementation of efficient algorithms to obtain acceptable solutions for the location of several facilities to serve customer sites. The general version of facility location problem is known to be NP-hard; For locating multiple facilities we use Voronoi diagram of initial facility locations to partition the customer sites into k clusters. On each Voronoi region, solutions for single facility problem is obtained by using both Weizfield\u27s algorithm and Center of Gravity. The customer space is again partitioned by using the newly computed locations. This iteration is continued to obtain a better solution for multi-facility location problem. We call the resulting algorithm: Voronoi driven k-median algorithm ; We report experimental results on several test data that include randomly distributed customers and distinctly clustered customers. The observed results show that the proposed approximation algorithm produces good results
Districting Problems - New Geometrically Motivated Approaches
This thesis focuses on districting problems were the basic areas are represented by points or lines. In the context of points, it presents approaches that utilize the problem\u27s underlying geometrical information. For lines it introduces an algorithm combining features of geometric approaches, tabu search, and adaptive randomized neighborhood search that includes the routing distances explicitly. Moreover, this thesis summarizes, compares and enhances existing compactness measures
Adaptive Algorithms for Coverage Control and Space Partitioning in Mobile Robotic Networks
We consider deployment problems where a mobile robotic network must optimize its configuration in a distributed way in order to minimize a steady-state cost function that depends on the spatial distribution of certain probabilistic events of interest. Three classes of problems are discussed in detail: coverage control problems, spatial partitioning problems, and dynamic vehicle routing problems. Moreover, we assume that the event distribution is a priori unknown, and can only be progressively inferred from the observation of the location of the actual event occurrences. For each problem we present distributed stochastic gradient algorithms that optimize the performance objective. The stochastic gradient view simplifies and generalizes previously proposed solutions, and is applicable to new complex scenarios, for example adaptive coverage involving heterogeneous agents. Finally, our algorithms often take the form of simple distributed rules that could be implemented on resource-limited platforms
Biased randomized insertion orders
In this thesis, we consider insertion orders for incremental construction in computational geometry. Specifically, we focus on Delaunay triangulations and arrangements of line segments. The starting point of this research was the assumption that by adapting the orders to the point sets, we could speed up the point location in incremental constructions. We present new insertion orders for Delaunay triangulations based on the concepts of adap-tive curves. More specifically, we explore orders that attempt to split the point set evenly in the recursive construction of the order. Further, we explore squarified orders that are orders that try to produce subproblems without any bias to one of the coordinate axes. We pro-vide implementations for all of these orders and several existing ones. We also propose new insertion orders for arrangements of line segments. We perform an experimental evaluation of the orders for incrementally constructing Delau-nay triangulations. Our experiments show the advantages of squarifying: for a tour visiting the points in the given order, the squarified order typically produces a shorter tour than the order it is based on. This results in (slightly) faster point location. The experiments also sho
Passive mobile data for studying seasonal tourism mobilities: an application in a Mediterranean Coastal destination
The article uses passive mobile data to analyse the complex mobilities that occur in a coastal
region characterised by seasonal patterns of tourism activity. A large volume of data generated by
mobile phone users has been selected and processed to subsequently display the information in the
form of visualisations that are useful for transport and tourism research, policy, and practice. More
specifically, the analysis consisted of four steps: (1) a dataset containing records for four days—two
on summer days and two in winter—was selected, (2) these were aggregated spatially, temporally,
and differentiating trips by local residents, national tourists, and international tourists, (3) origindestination matrices were built, and (4) graph-based visualisations were created to provide evidence
on the nature of the mobilities affecting the study area. The results of our work provide new evidence
of how the analysis of passive mobile data can be useful to study the effects of tourism seasonality in
local mobility patterns
Constructing Delaunay triangulations along space-filling curves
Incremental construction con BRIO using a space-filling curve order for insertion is a popular algorithm for constructing Delaunay triangulations. So far, it has only been analyzed for the case that a worst-case optimal point location data structure is used which is often avoided in implementations. In this paper, we analyze its running time for the more typical case that points are located by walking. We show that in the worst-case the algorithm needs quadratic time, but that this can only happen in degenerate cases. We show that the algorithm runs in O(n logn) time under realistic assumptions. Furthermore, we show that it runs in expected linear time for many random point distributions. This research was supported by the Deutsche Forschungsgemeinschaft within the European graduate program ’Combinatorics, Geometry, and Computation’ (No. GRK 588/2) and by the Netherlands’ Organisation for Scientific Research (NWO) under BRICKS/FOCUS grant number 642.065.503 and project no. 639.022.707
An Ab Initio Approach to the Solar Coronal Heating Problem
We present an ab initio approach to the solar coronal heating problem by
modelling a small part of the solar corona in a computational box using a 3D
MHD code including realistic physics. The observed solar granular velocity
pattern and its amplitude and vorticity power spectra, as reproduced by a
weighted Voronoi tessellation method, are used as a boundary condition that
generates a Poynting flux in the presence of a magnetic field. The initial
magnetic field is a potential extrapolation of a SOHO/MDI high resolution
magnetogram, and a standard stratified atmosphere is used as a thermal initial
condition. Except for the chromospheric temperature structure, which is kept
fixed, the initial conditions are quickly forgotten because the included
Spitzer conductivity and radiative cooling function have typical timescales
much shorter than the time span of the simulation. After a short initial start
up period, the magnetic field is able to dissipate 3-4 10^6 ergs cm^{-2} s^{-1}
in a highly intermittent corona, maintaining an average temperature of K, at coronal density values for which emulated images of the Transition
Region And Coronal Explorer(TRACE) 171 and 195 pass bands reproduce observed
photon count rates.Comment: 12 pages, 14 figures. Submitted to Ap
The Visibility Center of a Simple Polygon
We introduce the visibility center of a set of points inside a polygon - a point c_V such that the maximum geodesic distance from c_V to see any point in the set is minimized. For a simple polygon of n vertices and a set of m points inside it, we give an O((n+m) log (n+m)) time algorithm to find the visibility center. We find the visibility center of all points in a simple polygon in O(n log n) time.
Our algorithm reduces the visibility center problem to the problem of finding the geodesic center of a set of half-polygons inside a polygon, which is of independent interest. We give an O((n+k) log (n+k)) time algorithm for this problem, where k is the number of half-polygons
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