Abstract
Abstract Future Internet technologies and the deployment of mobile and nomadic services enable complex communications networks, that have a highly dynamic behavior. This naturally engenders route-discovery problems under changing conditions over these networks, but the temporal variations in the topology of dynamic networks are not effectively captured in a classical graph model. In this paper, we use evolving graphs, which help capture the dynamic characteristics of such networks, in order to compute multicast trees with minimum overall transmission time for a class of wireless mobile dynamic networks. We first show that computing different types of strongly connected components in evolving digraphs is NP-Hard, and then propose a polynomial-time algorithm to build all rooted directed Minimum Spanning Trees in strongly connected dynamic networks. These results open new avenues for the implementation of Internet spanning-tree based protocols over highly dynamic network infrastructures.
Highlights
With the advent of the Internet of Things, it is clear that a globally mobile Internet induces key new challenges related to existing communication and routing solutions [2]
The generalized case of mobile network routing using shortest paths or least cost methods are complicated by the arbitrary movement of the mobile agents thereby leading to random variations in link costs and connectivity [18]. This variable nature of the topology can be apprehended only by network updates of the link state between moving nodes, creating substantial communication overhead along the link. This naturally motivates studying the modeling of such dynamics, and designing algorithms that take it into account [19]
We focus on the analysis of connectivity properties in fixed schedule dynamic networks (FSDNs) and the design of algorithms for building directed minimal spanning trees (DMSTs) to generate multicast routes in FSDNs
Summary
With the advent of the Internet of Things, it is clear that a globally mobile Internet induces key new challenges related to existing communication and routing solutions [2]. Infrastructure-less mobile communication environments, such as mobile ad hoc networks (MANETs), present a paradigm shift from back-boned networks in that data are transferred from node to node via peer-to-peer interactions and not over an underlying backbone of routers This engenders new problems regarding optimal routing of data under various conditions over these dynamic networks [18]. The generalized case of mobile network routing using shortest paths or least cost methods are complicated by the arbitrary movement of the mobile agents thereby leading to random variations in link costs and connectivity [18] This variable nature of the topology can be apprehended only by network updates of the link state between moving nodes, creating substantial communication overhead along the link. If traversal times are discrete, the approach proposed in [11], namely of expanding the original graph into T layers representing the time steps
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