scholarly journals Competitive Online Routing on Delaunay Triangulations

2017 ◽  
Vol 27 (04) ◽  
pp. 241-253
Author(s):  
Prosenjit Bose ◽  
Jean-Lou De Carufel ◽  
Stephane Durocher ◽  
Perouz Taslakian
Keyword(s):  
Delaunay Triangulation ◽  
Shortest Path ◽  
Competitive Ratio ◽  
Routing Algorithm ◽  
Source Node ◽  
Point Sets ◽  
Target Node ◽  
Delaunay Triangulations ◽  
Online Routing ◽  
Set Of Points

Let [Formula: see text] be a graph, [Formula: see text] be a source node and [Formula: see text] be a target node. The sequence of adjacent nodes (graph walk) visited by a routing algorithm is a [Formula: see text]-competitive route if its length in [Formula: see text] is at most [Formula: see text] times the length of the shortest path from [Formula: see text] to [Formula: see text] in [Formula: see text]. We present a [Formula: see text]-competitive online routing algorithm on the Delaunay triangulation of an arbitrary given set of points in the plane. This improves the competitive ratio on Delaunay triangulations from the previous best of [Formula: see text]. We also present a [Formula: see text]-competitive online routing algorithm for Delaunay triangulations of point sets in convex position.

scholarly journals THE STABILITY OF DELAUNAY TRIANGULATIONS

2013 ◽  
Vol 23 (04n05) ◽  
pp. 303-333 ◽  
Author(s):  
JEAN-DANIEL BOISSONNAT ◽  
RAMSAY DYER ◽  
ARIJIT GHOSH
Keyword(s):  
Delaunay Triangulation ◽  
Point Sets ◽  
Generic Point ◽  
Delaunay Triangulations ◽  
Delaunay Simplices ◽  
The Stability

We introduce a parametrized notion of genericity for Delaunay triangulations which, in particular, implies that the Delaunay simplices of δ-generic point sets are thick. Equipped with this notion, we study the stability of Delaunay triangulations under perturbations of the metric and of the vertex positions. We quantify the magnitude of the perturbations under which the Delaunay triangulation remains unchanged.

scholarly journals IMPROVING SHORTEST PATHS IN THE DELAUNAY TRIANGULATION

2012 ◽  
Vol 22 (06) ◽  
pp. 559-576
Author(s):  
MANUEL ABELLANAS ◽  
MERCÈ CLAVEROL ◽  
GREGORIO HERNÁNDEZ ◽  
FERRAN HURTADO ◽  
VERA SACRISTÁN ◽  
...  
Keyword(s):  
Delaunay Triangulation ◽  
Shortest Path ◽  
Shortest Paths ◽  
Efficient Algorithms ◽  
Graph Distance ◽  
Delaunay Triangulations ◽  
Link Distance ◽  
Point Set

We study a problem about shortest paths in Delaunay triangulations. Given two nodes s, t in the Delaunay triangulation of a point set S, we look for a new point p ∉ S that can be added, such that the shortest path from s to t, in the Delaunay triangulation of S∪{p}, improves as much as possible. We study several properties of the problem, and give efficient algorithms to find such a point when the graph-distance used is Euclidean and for the link-distance. Several other variations of the problem are also discussed.

A Recursive Shortest Path Routing Algorithm With Application for Wireless Sensor Network Localization

2016 ◽  
Vol 16 (11) ◽  
pp. 4631-4637 ◽  
Author(s):  
Juan Cota-Ruiz ◽  
Pablo Rivas-Perea ◽  
Ernesto Sifuentes ◽  
Rafael Gonzalez-Landaeta
Keyword(s):  
Wireless Sensor Network ◽  
Sensor Network ◽  
Shortest Path ◽  
Routing Algorithm ◽  
Wireless Sensor ◽  
Sensor Network Localization ◽  
Shortest Path Routing ◽  
Network Localization

scholarly journals MAINTAINING VISIBILITY INFORMATION OF PLANAR POINT SETS WITH A MOVING VIEWPOINT

2007 ◽  
Vol 17 (04) ◽  
pp. 297-304 ◽  
Author(s):  
OLIVIER DEVILLERS ◽  
VIDA DUJMOVIĆ ◽  
HAZEL EVERETT ◽  
SAMUEL HORNUS ◽  
SUE WHITESIDES ◽  
...  
Keyword(s):  
Linear Space ◽  
Point Sets ◽  
Worst Case ◽  
Planar Point ◽  
Set Of Points

Given a set of n points in the plane, we consider the problem of computing the circular ordering of the points about a viewpoint q and efficiently maintaining this ordering information as q moves. In linear space, and after O(n log n) preprocessing time, our solution maintains the view at a cost of O( log n) amortized time (resp.O( log 2 n) worst case time) for each change. Our algorithm can also be used to maintain the set of points sorted according to their distance to q .

scholarly journals An Efficient Anonymous Communication Scheme to Protect the Privacy of the Source Node Location in the Internet of Things

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Fengyin Li ◽  
Pei Ren ◽  
Guoyu Yang ◽  
Yuhong Sun ◽  
Yilei Wang ◽  
...  
Keyword(s):  
Wireless Sensor Networks ◽  
Sensor Networks ◽  
Location Privacy ◽  
Routing Algorithm ◽  
Residual Energy ◽  
Source Node ◽  
Wireless Sensor ◽  
Anonymous Communication ◽  
Privacy Leakage ◽  
Communication Scheme

Advances in machine learning (ML) in recent years have enabled a dizzying array of applications such as data analytics, autonomous systems, and security diagnostics. As an important part of the Internet of Things (IoT), wireless sensor networks (WSNs) have been widely used in military, transportation, medical, and household fields. However, in the applications of wireless sensor networks, the adversary can infer the location of a source node and an event by backtracking attacks and traffic analysis. The location privacy leakage of a source node has become one of the most urgent problems to be solved in wireless sensor networks. To solve the problem of source location privacy leakage, in this paper, we first propose a proxy source node selection mechanism by constructing the candidate region. Secondly, based on the residual energy of the node, we propose a shortest routing algorithm to achieve better forwarding efficiency. Finally, by combining the proposed proxy source node selection mechanism with the proposed shortest routing algorithm based on the residual energy, we further propose a new, anonymous communication scheme. Meanwhile, the performance analysis indicates that the anonymous communication scheme can effectively protect the location privacy of the source nodes and reduce the network overhead.

Upper and Lower Bounds for Online Routing on Delaunay Triangulations

2015 ◽  
pp. 203-214 ◽  
Author(s):  
Nicolas Bonichon ◽  
Prosenjit Bose ◽  
Jean-Lou De Carufel ◽  
Ljubomir Perković ◽  
André van Renssen
Keyword(s):  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Delaunay Triangulations ◽  
Online Routing

Resource Efficient Online Routing Enabled Translucent Space Division Multiplexing Based Elastic Optical Networks

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Sridhar Iyer
Keyword(s):  
Optical Networks ◽  
Blocking Probability ◽  
Optical Network ◽  
Routing Algorithm ◽  
Network Resources ◽  
Modulation Formats ◽  
Modulation Format ◽  
Online Routing ◽  
Space Division Multiplexing ◽  
Space Division

AbstractIn the current work, we focus on the optimization of lightpath routing in a Space Division Multiplexing based Elastic Optical Network (SDM-b-EON) for which we propose an online routing algorithm, named as Resource Efficient Online Routing Algorithm with Regeneration (REORAwR) which, in addition to ensuring the routing of translucent lightpaths through spectral super-channels over spatial modes links also accounts for the presence of the transceivers in the network. The proposed REORAwR algorithm is tunable such that it can either aim to reduce the bandwidth blocking probability or can aim to minimize the overall consumed power. In regard to regeneration, we investigate two scenarios which differ in their regeneration variability level in addition to the adjustment of modulation formats as per the transmission route characteristics. We conduct extensive simulations considering two realistic network topologies and realistic transmission reach values. The obtained results demonstrate that significant benefits can be obtained in regard to the utilization of both the major network resources (spectrum and transceivers) when regeneration is conducted with complete flexibility and modulation format conversion is also permitted at every node of the SDM-b-EON. In addition, the obtained results also show that when compared to spectrum usage, in terms of the overall consumed power, the performance profits which can be obtained in a translucent SDM-b-EON are very small.

OPTIMUM CONGESTED ROUTING STRATEGY ON TWISTED CUBES

2000 ◽  
Vol 01 (02) ◽  
pp. 115-134 ◽  
Author(s):  
TSENG-KUEI LI ◽  
JIMMY J. M. TAN ◽  
LIH-HSING HSU ◽  
TING-YI SUNG
Keyword(s):  
Shortest Path ◽  
Time Complexity ◽  
Interconnection Network ◽  
Routing Algorithm ◽  
Optimum Time ◽  
Shortest Path Routing ◽  
Routing Strategy ◽  
Bisection Width ◽  
Twisted Cube ◽  
Twisted Cubes

Given a shortest path routing algorithm of an interconnection network, the edge congestion is one of the important factors to evaluate the performance of this algorithm. In this paper, we consider the twisted cube, a variation of the hypercube with some better properties, and review the existing shortest path routing algorithm8. We find that its edge congestion under the routing algorithm is high. Then, we propose a new shortest path routing algorithm and show that our algorithm has optimum time complexity O(n) and optimum edge congestion 2n. Moreover, we calculate the bisection width of the twisted cube of dimension n.

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