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Asymptotic properties of Euclidean shortest-path trees in random geometric graphs

Christian Hirsch, David Neuhäuser, Catherine Gloaguen, Volker Schmidt
2015 Statistics and Probability Letters  
We consider asymptotic properties of two functionals on Euclidean shortest-path trees appearing in random geometric graphs in R 2 which can be used, for example, as models for fixed-access telecommunication  ...  The corresponding Voronoi tessellation is generated by a stationary Cox process which is concentrated on the edges of the random geometric graph and whose intensity tends to 0.  ...  To be more precise, for x, y ∈ G * let ρ(x, y) denote a shortest path in the graph G * connecting x and y.  ... 
doi:10.1016/j.spl.2015.08.012 fatcat:b6vc6s4oo5fptf5zxwysrxf33e

Shortest Paths In Euclidean Graphs

R. Sedgewick, J.S. Vitter
25th Annual Symposium onFoundations of Computer Science, 1984.  
We analyze a simple method for finding shortest paths in Euclidean graphs (where vertices are points in a Euclidean space and edge weights are distances between points).  ...  For many graph models, the running time of the algorithm to find the shortest path between a specified pair of vertices in a graph with V vertices and E edges is shown to be O ( V ) as compared with O(  ...  In this case, the spanning tree is a 'shortest path tree" which defines the shortest path in the graph shortest path from s t o t , we assign a high priority to s at the beginning to make it the start  ... 
doi:10.1109/sfcs.1984.715943 dblp:conf/focs/SedgewickV84 fatcat:vvdggikdffe5piek4gdeqydeo4

A generalized hypergreedy algorithm for weighted perfect matching

Celina Imielinska, Bahman Kalantari
1993 BIT Numerical Mathematics  
With a modified version of this algorithm we obtain a log n-approximate perfect matching heuristic for points in the Euclidean plane, in O(n log z n) time.  ...  We give a generalization of the hypergreedy algorithm for minimum weight perfect matching on a complete edge weighted graph whose weights satisfy the triangle inequality.  ...  In particular, we thank one of the referees for making us aware of the recent result by Keil and Gutwin [8] which allowed us to improve the error bound of our heuristic, originally based on Chew's result  ... 
doi:10.1007/bf01989743 fatcat:wsd7j5vlmnhqjooa5bkol6ecli

Approximating the Stretch Factor of Euclidean Graphs

Giri Narasimhan, Michiel Smid
2000 SIAM journal on computing (Print)  
However, if an approximation to the stretch factor is sufficient, then we show it can be efficiently computed by making only O(n) approximate shortest path queries in the graph G.  ...  It can trivially be solved by solving the All-Pairs-Shortest-Path problem.  ...  For any graph G in this class, we can, after an O(n)-time preprocessing, answer exact shortest path queries in O(1) time, if G is a path or cycle, and in O(log n) time, if G is a tree.  ... 
doi:10.1137/s0097539799361671 fatcat:yfy67d5sqrakjnupd5kviksxdm

First Passage Percolation on Random Geometric Graphs and an Application to Shortest-Path Trees

C. Hirsch, D. Neuhäuser, C. Gloaguen, V. Schmidt
2015 Advances in Applied Probability  
In particular, we establish a strong linear growth property for shortest-path lengths on random geometric graphs which are generated by point processes.  ...  We consider Euclidean first passage percolation on a large family of connected random geometric graphs in the d-dimensional Euclidean space encompassing various well-known models from stochastic geometry  ...  G n (X ). for fixed n ≥ 2 define G n (X ) = (V , E), Tail bounds for shortest-path lengths nearest point on graph: q(x) = argmin y ∈G |x − y | length of shortest Euclidean path on G: where V = X {x, y  ... 
doi:10.1239/aap/1435236978 fatcat:xwno776zqjbe3jp44o7jyv3d54

Review of visibility algorithms in the plane by Subir Kumar Ghosh (Cambridge University Press, 2007)

Alice M. Dean
2009 ACM SIGACT News  
The answer, given first by Chvátal [3] and later by Fisk [5], using an elegant graph-theoretic proof, is that n/3 guards are always sufficient and may be necessary.  ...  Posed by Victor Klee in 1973, it asks how many stationary guards are required to see all points in an art gallery represented by a simple, n-sided polygon.  ...  In addition, the chapter gives algorithms for recognizing special classes of visibility graphs. • Chapter 7 Visibility and Link Paths: In contrast to a Euclidean shortest path in a polygon P , a minimum  ... 
doi:10.1145/1556154.1556163 fatcat:iozevnuohncx5pbzpkntvj4fn4

AutoDrone: Shortest Optimized Obstacle-Free Path Planning for Autonomous Drones [article]

Prithwish Jana, Debasish Jana
2021 arXiv   pre-print
We propose a method to find out the shortest obstacle-free path in the coordinate system guided by GPS.  ...  Our approach can be especially beneficial in rescue operations and fast delivery or pick-up in an energy-efficient way, where our algorithm will help in finding out the shortest path and angle along which  ...  And the task for the AutoDrone boils down to the task to find the single-source shortest path in a directed graph in Euclidean space.  ... 
arXiv:2111.00200v2 fatcat:d5b62sil4ffxplnymizlmoc4dq

ROUTING URBAN TRANSPORT NETWORK WITH WEIGHING ARCS FUZZY NUMBERS AND APPLICATION IN EMERGENCY MEDICAL AID

Petya Stoyanova
2017 Applied Researches in Technics, Technologies and Education  
The network is represented as a directed graph with Fuzzy arcs' weights and travel times as a function of traffic flows.  ...  The target function and constraints and binary variables are defined in the Solver Add-in.  ...  ARTTE Applied Researches in Technics, Technologies and Education Journal of the Faculty of Technics and Technologies, Trakia University https://sites.google.com/a/trakia-uni.bg/artte/  ... 
doi:10.15547/artte.2017.01.002 fatcat:eevkknxy6vhvlargir5uvzitjm

Making Explainable Friend Recommendations Based on Concept Similarity Measurements via a Knowledge Graph

Shaohua Tao, Runhe Qiu, Yuan Ping, Woping Xu, Hui Ma
2020 IEEE Access  
INDEX TERMS Knowledge graph, similarity measurement, semantic similarity, the shortest path, Euclidean-shortest path, imbalance structure.  ...  Then we designed a novel Weighted Euclidean-Shortest Path (WESP) method for measuring concept similarity in a knowledge graph and applied it to friend recommendations on a microblogging platform.  ...  THE SHORTEST PATH-GUIDED REASONING AND THE WEIGHTED EUCLIDEAN-SHORTEST PATH A.  ... 
doi:10.1109/access.2020.3014670 fatcat:clfruj4jt5djrp7pi4aqx4o6uq

Fast and Scalable Analysis of Massive Social Graphs [article]

Xiaohan Zhao, Alessandra Sala, Haitao Zheng, Ben Y. Zhao
2011 arXiv   pre-print
After a one- time preprocessing cost, Rigel answers node-distance queries in 10's of microseconds, and also produces shortest path results up to 18 times faster than prior shortest-path systems with similar  ...  Finally, we show that Rigel's functionality can be easily extended to locate (near-) shortest paths between node pairs.  ...  For example, the shortest path distance between nodes A and B is 3 in the graph (left), and the Euclidean distance between their coordinates is 3.1 (right). graph size.  ... 
arXiv:1107.5114v2 fatcat:qprwirknqvay5dbyvc2jtsvpby

Landmark Guided Probabilistic Roadmap Queries [article]

Brian Paden, Yannik Nager, Emilio Frazzoli
2017 arXiv   pre-print
The heuristic is generated by storing minimum spanning trees from a small number of vertices within the graph and using these trees to approximate the cost of a shortest path between any two vertices of  ...  the graph.  ...  Algorithm 2 summarizes the A * algorithm for finding a shortest path in the PRM graph fromx 0 tox g .  ... 
arXiv:1704.01886v1 fatcat:fjh3mmsqgfhd5msphrmh3cyc7y

The FastMap Algorithm for Shortest Path Computations [article]

Liron Cohen, Tansel Uras, Shiva Jahangiri, Aliyah Arunasalam, Sven Koenig, T.K. Satish Kumar
2017 arXiv   pre-print
The Euclidean distance between any two nodes in this space approximates the length of the shortest path between them in the given graph.  ...  Later, at runtime, a shortest path between any two nodes can be computed with A* search using the Euclidean distances as heuristic.  ...  The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the sponsoring organizations  ... 
arXiv:1706.02792v3 fatcat:ov6ja7pjtbdvpk33li2vcxjabu

Delineating imprecise regions via shortest-path graphs

Mark de Berg, Wouter Meulemans, Bettina Speckmann
2011 Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems - GIS '11  
We use shortest-path graphs based on the squared Euclidean distance which capture the shape of region boundaries well.  ...  Shortest-path graphs naturally adapt to point sets of varying density, and they are always connected.  ...  Therefore, any edge of the shortest-path graph with squared Euclidean distance must be present in the Gabriel graph: the shortest-path graph is thus a subset of the Gabriel graph.  ... 
doi:10.1145/2093973.2094010 dblp:conf/gis/BergMS11 fatcat:uttcwodipfdu7b7cxsp6ohlr3y

The FastMap Algorithm for Shortest Path Computations

Liron Cohen, Tansel Uras, Shiva Jahangiri, Aliyah Arunasalam, Sven Koenig, T. K. Satish Kumar
2018 Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence  
The Euclidean distance between any two nodes in this space approximates the length of the shortest path between them in the given graph.  ...  Later, at runtime, a shortest path between any two nodes can be computed with an A* search using the Euclidean distances as heuristic.  ...  The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the sponsoring organizations  ... 
doi:10.24963/ijcai.2018/198 dblp:conf/ijcai/0002UJAKK18 fatcat:w2llywyiyreyjcxay2wjxrpcve

A survey of geodesic paths on 3D surfaces

Prosenjit Bose, Anil Maheshwari, Chang Shu, Stefanie Wuhrer
2011 Computational geometry  
This survey gives a brief overview of theoretically and practically relevant algorithms to compute geodesic paths and distances on three-dimensional surfaces.  ...  As in previous approaches, the approach proceeds by constructing a graph and by computing the shortest path between vertices of a graph.  ...  In the first stage, a 3D length estimator is used in a graph search on the graph defined by the surface voxels to find a global approximation of the shortest path.  ... 
doi:10.1016/j.comgeo.2011.05.006 fatcat:rms6kzrlkfb4baf3pfz6obpzyi
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