About the Point Location Problem

Handbook of Research on Geoinformatics ◽

10.4018/978-1-59140-995-3.ch013 ◽

2010 ◽

pp. 100-105

Author(s):

José Poveda ◽

Michael Gould

Keyword(s):

Location Problem ◽

Computational Cost ◽

Point Location ◽

Location Algorithm

In this chapter we present some well-known algorithms for the solution of the point location problem and for the more particular problem of point-in-polygon determination. These previous approaches to the problem are presented in the first sections. In the remainder of the paper, we present a quick location algorithm based on a quaternary partition of the space, as well as its associated computational cost.

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2D Triangulation of Signals Source by Pole-Polar Geometric Models

Sensors ◽

10.3390/s19051020 ◽

2019 ◽

Vol 19 (5) ◽

pp. 1020 ◽

Cited By ~ 2

Author(s):

Aleksandro Montanha ◽

Airton M. Polidorio ◽

F. J. Dominguez-Mayo ◽

María J. Escalona

Keyword(s):

Location Problem ◽

Computational Cost ◽

Navigation Systems ◽

Point Location ◽

New Approach ◽

Geometric Models ◽

Machine Learning Methods ◽

Points Of Interest ◽

Polar Geometry ◽

Geometric Relationship

The 2D point location problem has applications in several areas, such as geographic information systems, navigation systems, motion planning, mapping, military strategy, location and tracking moves. We aim to present a new approach that expands upon current techniques and methods to locate the 2D position of a signal source sent by an emitter device. This new approach is based only on the geometric relationship between an emitter device and a system composed of m≥2 signal receiving devices. Current approaches applied to locate an emitter can be deterministic, statistical or machine-learning methods. We propose to perform this triangulation by geometric models that exploit elements of pole-polar geometry. For this purpose, we are presenting five geometric models to solve the point location problem: (1) based on centroid of points of pole-polar geometry, PPC; (2) based on convex hull region among pole-points, CHC; (3) based on centroid of points obtained by polar-lines intersections, PLI; (4) based on centroid of points obtained by tangent lines intersections, TLI; (5) based on centroid of points obtained by tangent lines intersections with minimal angles, MAI. The first one has computational cost On and whereas has the computational cost Onlognwhere n is the number of points of interest.

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A new point-location algorithm and its practical efficiency: comparison with existing algorithms

ACM Transactions on Graphics ◽

10.1145/357337.357338 ◽

1984 ◽

Vol 3 (2) ◽

pp. 86-109 ◽

Cited By ~ 40

Author(s):

Ta. Asano

Keyword(s):

Point Location ◽

Location Algorithm ◽

Efficiency Comparison

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Subsurface reflectivity estimation from imaging of primaries and multiples using amplitude-normalized separated wavefields

Geophysics ◽

10.1190/geo2015-0385.1 ◽

2016 ◽

Vol 81 (3) ◽

pp. S101-S117 ◽

Cited By ~ 2

Author(s):

Alba Ordoñez ◽

Walter Söllner ◽

Tilman Klüver ◽

Leiv J. Gelius

Keyword(s):

Integral Equation ◽

Fredholm Integral Equation ◽

Computational Cost ◽

Image Point ◽

Point Location ◽

Multiple Reflections ◽

Frequency Space ◽

Propagation Effects ◽

The Matrix ◽

Spatial Domains

Several studies have shown the benefits of including multiple reflections together with primaries in the structural imaging of subsurface reflectors. However, to characterize the reflector properties, there is a need to compensate for propagation effects due to multiple scattering and to properly combine the information from primaries and all orders of multiples. From this perspective and based on the wave equation and Rayleigh’s reciprocity theorem, recent works have suggested computing the subsurface image from the Green’s function reflection response (or reflectivity) by inverting a Fredholm integral equation in the frequency-space domain. By following Claerbout’s imaging principle and assuming locally reacting media, the integral equation may be reduced to a trace-by-trace deconvolution imaging condition. For a complex overburden and considering that the structure of the subsurface is angle-dependent, this trace-by-trace deconvolution does not properly solve the Fredholm integral equation. We have inverted for the subsurface reflectivity by solving the matrix version of the Fredholm integral equation at every subsurface level, based on a multidimensional deconvolution of the receiver wavefields with the source wavefields. The total upgoing pressure and the total filtered downgoing vertical velocity were used as receiver and source wavefields, respectively. By selecting appropriate subsets of the inverted reflectivity matrix and by performing an inverse Fourier transform over the frequencies, the process allowed us to obtain wavefields corresponding to virtual sources and receivers located in the subsurface, at a given level. The method has been applied on two synthetic examples showing that the computed reflectivity wavefields are free of propagation effects from the overburden and thus are suited to extract information of the image point location in the angular and spatial domains. To get the computational cost down, our approach is target-oriented; i.e., the reflectivity may only be computed in the area of most interest.

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An efficientg-centroid location algorithm for cographs

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/ijmms.2005.1405 ◽

2005 ◽

Vol 2005 (9) ◽

pp. 1405-1413 ◽

Cited By ~ 1

Author(s):

V. Prakash

Keyword(s):

Location Problem ◽

Maximum Clique ◽

Polynomial Time Algorithm ◽

Time Algorithm ◽

Outerplanar Graphs ◽

Arbitrary Graph ◽

Maximal Outerplanar Graphs ◽

Split Graphs ◽

Location Algorithm ◽

Centroid Location

In 1998, Pandu Rangan et al. Proved that locating theg-centroid for an arbitrary graph is𝒩𝒫-hard by reducing the problem of finding the maximum clique size of a graph to theg-centroid location problem. They have also given an efficient polynomial time algorithm for locating theg-centroid for maximal outerplanar graphs, Ptolemaic graphs, and split graphs. In this paper, we present anO(nm)time algorithm for locating theg-centroid for cographs, wherenis the number of vertices andmis the number of edges of the graph.

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