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

Abstract

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

Adaptive transmission power level algorithm according to random deployment of nodes in WSN

“…𝑑(𝑛 𝑗 ) 𝑚(𝑖) = √ (𝑥 𝑛𝑜𝑑𝑒 𝑛 − 𝑥 𝑛𝑜𝑑𝑒 𝑚(𝑖) ) 2 + (𝑦 𝑛𝑜𝑑𝑒 𝑛 − 𝑦 𝑛𝑜𝑑𝑒 𝑚(𝑖) ) 2 …(10) 𝐷_𝐸𝑟𝑟𝑜𝑟(𝑛 𝑗 ) = 𝑀𝑖𝑛(𝑑(𝑛 𝑗 ) 𝑚(1) , 𝑑(𝑛 𝑗 ) 𝑚(2) , … , 𝑑(𝑛 𝑗 ) 𝑚(𝑚) ) …(11) …”