Abstract
The computation of a set constituted by few vertices to define a virtual backbone supporting information interchange is a problem that arises in many areas when analysing networks of different natures, like wireless, brain, or social networks. Recent papers propose obtaining such a set of vertices by computing the connected dominating set (CDS) of a graph. In recent works, the CDS has been obtained by considering that all vertices exhibit similar characteristics. However, that assumption is not valid for complex networks in which their vertices can play different roles. Therefore, we propose finding the CDS by taking into account several metrics which measure the importance of each network vertex e.g., error probability, entropy, or entropy variation (EV).
Highlights
Complex networks are playing an increasingly important role in a large number of areas [1,2]
We have considered an ad hoc wireless network which is a decentralized type of wireless network characterized by a lack of fixed communication infrastructure, so that the selection of vertices forwarding data is dynamically made by considering the current network connectivity
In this paper we proposed selecting the connected dominating set (CDS) of a graph by incorporating vertex importance metrics defined in order to maximize a desired cost function such as error probability, entropy, or entropy variation
Summary
Complex networks are playing an increasingly important role in a large number of areas (for instance, biology, physics, Social Science, etc.) [1,2]. Connected dominating sets (CDSs) are natural candidates for vertices to be used for information interchange in any kind of network. More recently in [15] the authors proposed including a new condition to the MWCDS of a UDG: all vertices in the MWDS must be connected with k vertices to guarantee redundancy All these algorithms were designed for the UDG without taking into account the condition of minimizing the dominant size. In a recent paper, Ai [20] introduced the concept of entropy variation as a measurement of the influence of each vertex in the graph In this sense, our study is oriented towards finding an MWCDS considering that graph information.
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