LPCN: Least polar-angle connected node algorithm to find a polygon hull in a connected euclidean graph

Lalem, Farid; Bounceur, Ahcène; Bezoui, Madani; Saoudi, Massinissa; Euler, Reinhardt; Kechadi, Tahar; Sevaux, Marc

doi:10.1016/j.jnca.2017.05.005

Cited by 9 publications

(9 citation statements)

References 30 publications

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“…Saoudi et al [51] have presented a distributed version of the LPCN (Least Polar-angle Connected Node) algorithm introduced in [36]. In each iteration, the current boundary node chooses the nearest polar angle given by the previously chosen node and its neighbors, and the first node has to be a boundary node.…”

Section: Boundary Node Detection In Wireless Sensor Networkmentioning

confidence: 99%

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Finding the polygon hull of a network without conditions on the starting vertex

Bounceur

Bezoui

Hammoudeh

et al. 2019

Trans Emerging Tel Tech

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Many real-life problems arising within the fields of wireless communication, image processing, combinatorial optimisation, etc., can be modeled by means of Euclidean graphs. In the case of Wireless Sensor Networks (WSN), the overall topology of the graph is not known, because sensor nodes are often randomly deployed. One of the significant problems in this field is the search for boundary nodes. This problem is important in cases such as the surveillance of an area of interest, image contour reconstruction, graph matching problems, routing or clustering data, etc. In the literature, many algorithms are proposed to solve this problem, a recent one of which is the LPCN algorithm and its distributed version D-LPCN which are both based on the concept of a polar angle visit. An inconvenience of these algorithms is the determination of the starting vertex. In effect, the point with the minimum x-coordinate is a possible starting point but it has to be known at the beginning which considerably increases the algorithms' complexity. In this article, we propose a new method called RRLPCN (Reset and Restart with Least Polar-angle Connected Node) which is based on the LPCN algorithm to find the boundary vertices of a Euclidean graph. The main idea is to start the LPCN algorithm from an arbitrary vertex and, whenever it finds a vertex with an x-coordinate smaller than that of the starting one, LPCN is reset and restarted from this new vertex. The algorithm stops as soon as it visits the

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Section: Boundary Node Detection In Wireless Sensor Networkmentioning

confidence: 99%

“…This process is repeated until a polar angle is traversed for the second time. Despite the good performance of this algorithm and its optimality, demonstrated in the work of Lalem et al, 7 it requires an a priori knowledge of the starting vertex, which considerably increases its complexity.…”

Section: Introductionmentioning

confidence: 99%

Finding the polygon hull of a network without conditions on the starting vertex

Bounceur

Bezoui

Hammoudeh

et al. 2019

Trans Emerging Tel Tech

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“…Since the proposed algorithm D-LPCN represents the distributed version of LPCN, we will briefly present in this section the LPCN algorithm used to find the polygon hull in a connected Euclidean graph that we have presented in [1,30] and where we have proven its optimality and its convergence. This problem can be formulated as follows.…”

Section: Lpcn Algorithmmentioning

confidence: 99%

“…and v i−1 is the vertex of the polygon hull found in the previous iteration i − 1. This algorithm covers some problematic situations whose treatment is illustrated in our paper [30]. One of these situations is given by a pair of intersecting edges in the graph G. By definition of a polygon hull, no two edges of a polygon hull should intersect.…”

Section: Lpcn Algorithmmentioning

confidence: 99%

D-LPCN: A distributed least polar-angle connected node algorithm for finding the boundary of a wireless sensor network

et al. 2017

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A boundary of wireless sensor networks (WSNs) can be used in many fields, for example, to monitor a frontier or a secure place of strategic sensitive sites like oil fields or frontiers of a country. This situation is modeled as the problem of finding a polygon hull in a connected Euclidean graph, which represents a minimal set of connected boundary nodes. In this paper we propose a new algorithm called D-LPCN (Distributed Least Polar-angle Connected Node) which represents the distributed version of the LPCN algorithm introduced in [1]. In each iteration, any boundary node, except the first one, chooses its nearest polar angle node among its neighbors with respect to the node found in the previous iteration. The first starting node can be automatically determined using the Minimum Finding algorithm, which has two main advantages. The first one is that the algorithm works with any type of a connected network, given as planar or not. Furthermore, it takes into account any blocking situation and contains the necessary elements to avoid them. The second advantage is that the algorithm can determine all the boundaries of the different connected parts of the network. The proposed algorithm is validated using the CupCarbon, Tossim and Contiki simulators. It has also been implemented using real sensor nodes based on the TelosB and Arduino/XBee platforms. We have estimated the energy consumption of each node and we have found that the consumption of the network depends on the number of the boundary nodes and their neighbors. The simulation results show that the proposed algorithm is less energy consuming than the existing algorithms and its distributed version is less energy consuming than the centralized version.

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“…In the case of routing, it can be the highest level or the lowest level of energy. In case of the D-LPCN [8,12], it is the node that starts the algorithm, which is the node having the minimum x-coordinate. Houses can also be equipped with sensors and applications used to adapt the temperature and the brightness automatically depending on the outside weather.…”

Section: Introduction and Related Workmentioning

confidence: 99%

A New Leader Election Algorithm based on the WBS Algorithm Dedicated to Smart-cities

Kadjouh

Bounceur

Tari

et al. 2019

Proceedings of the 3rd International Conference on Future Networks and Distributed Systems

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One of the interesting techniques for leader election is used in the WBS (Wait Before Starting) algorithm, in which each node in the network will wait for a time corresponding to its value before starting to send the first message to neighbours. This means that the node with the smallest value becomes the leader and it also starts first. This approach is impracticable in the case of real values (case of GPS-coordinates). Also, if the values are very large, the waiting time becomes too long. In this paper, we propose a fast, fault-tolerant and low energy leader election algorithm dedicated to smart-cities, which is based on the technique of waiting before starting, with minimum complexity and in which every node sends one and only one message. Here, the leader is the node with the smallest x-coordinate and the total of sent and received messages is used to represent the global consumption in the network. We give a detailed description of the algorithm, prove its accuracy, discuss its complexity in terms of exchanged messages and evaluate its performance using the CupCarbon simulator. We show that our algorithm is well balanced in terms of energy consumption, it is efficient and adapts well to the increase of the nodes number in the network.

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LPCN: Least polar-angle connected node algorithm to find a polygon hull in a connected euclidean graph

Cited by 9 publications

References 30 publications

Finding the polygon hull of a network without conditions on the starting vertex

Finding the polygon hull of a network without conditions on the starting vertex

D-LPCN: A distributed least polar-angle connected node algorithm for finding the boundary of a wireless sensor network

A New Leader Election Algorithm based on the WBS Algorithm Dedicated to Smart-cities

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