Convergecast Tree on Temporal Graphs

Abstract

Temporal graphs are useful tools to model dynamic network topologies found in many applications. In this paper, we address the problem of constructing a convergecast tree on temporal graphs for data collection in dynamic sensor networks. Two types of convergecast trees, bounded arrival time convergecast tree and minimum total arrival time convergecast tree are defined as useful structures for low delay data collection. An [Formula: see text] time centralized algorithm is proposed to construct a bounded arrival time convergecast tree, where [Formula: see text] is the number of nodes, [Formula: see text] is the number of edges, and [Formula: see text] is the lifetime of the given temporal graph. The algorithm presented is an offline algorithm and assumes that all information about change in the graph topology is known apriori. It is then shown that the problem of constructing a minimum total arrival time convergecast tree is NP-complete, and an [Formula: see text] time centralized, offline heuristic algorithm is proposed to address it. The heuristic algorithm is evaluated with experiments on four real life data sets.