In practice, an alliance can be a bond or connection between individuals, families, states, or entities, etc. Formally, a non-empty set S of vertices of a graph G is a defensive k-alliance (resp. an offensive k-alliance) if every vertex of S (resp. the boundary of S) has at least k more neighbors inside of S than it has outside of S. A powerful k-alliance is both defensive k-alliance and offensive (k+2)alliance. During the last decade there has been a remarkable development on these three kinds of alliances. Due to their variety of applications, the alliances in its broad sense have received a special attention from many scientists and researchers. There have been applications of alliances in several areas such as bioinformatics, distributed computing, web communities, social networks, data clustering, business, etc. Several k-alliance numbers have been defined and a huge number of theoretical (algorithmic and computational) results are obtained for various graph classes. In this paper, we present a survey which covers a number of practical applications of alliances and the vast mathematical properties of the three types of k-alliances by giving a special attention to the study of the associated k-alliance (partition) numbers for different graph classes. c
A vehicular ad hoc network (VANET) is composed mainly of fixed roadside entities (RSUs) and mobile entities (vehicles). In order to exchange information and data relating to the safety and comfort of road users, these different entities must establish communications between them. In these communications, one of the main problems is related to congestion and saturation of RSUs. In this paper, we first study the main protocols that involve RSUs in their strategy of routing by classifying them according to four levels. Furthermore, to deal with the problem of saturation of RSUs, we present a new approach of cooperation between the RSUs of a VANET in order to reduce its congestion and avoid as much as possible the saturation of these entities. This approach, called "D2A2RS" (defensive alliance-based approach for reducing RSUs saturation), is based on the concept of defensive alliances in graphs that ensures effective collaboration between RSUs. To evaluate the performance of the proposed approach, we conduct a comparative analysis by using both analytical models and simulations. The obtained comparison results have shown the efficiency and the performance of our approach compared with other concurrent approaches in the literature in terms of packet loss/success rate, end-to-end transmission delay, and network scalability. KEYWORDSanalytical model, congestion, cooperation, defensive alliance of data processing, roadside unit (RSU), saturation, simulation, vehicular ad hoc network (VANET) Int J Commun Syst. 2020;33:e4245.wileyonlinelibrary.com/journal/dac
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