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The contribution of this paper is threefold. First, we give tight bounds for the complexity of the problem of data aggregation in static networks. In more details, we show that the problem remains NP-complete when the graph is of degree at most three. Second, we investigate the complexity of the same problem in a dynamic network, that is, a network whose topology can evolve through time. In the case of dynamic networks, we show that the problem is NP-complete even in the case where the graph is of degree at most two. Third, we give the first lower and upper bounds for the minimum data aggregation time in a dynamic graph. We also observe that even in a well-connected evolving graphs, the optimal solution cannot be found by a distributed algorithm or by a centralized algorithm that does not know the future. [ABSTRACT FROM AUTHOR]

We investigate exploration algorithms for autonomous mobile robots evolving in uniform ring-shaped networks. Unlike previous works, we consider myopia (each robot can only observe its neighboring nodes) and luminosity (each robot can use only two colors for its light) properties for the robots. As a main contribution, we prove that (i) in the FSYNC model, two (resp. three) myopic robots are necessary and sufficient to achieve perpetual (resp. terminating) exploration, and (ii) in the SSYNC and ASYNC models, three (resp. four) myopic robots are necessary and sufficient to achieve perpetual (resp. terminating) exploration. We also show that, in all execution models, our perpetual exploration algorithm is universal. That is, the algorithm solves perpetual exploration from any solvable initial configuration with two (resp. three) myopic robots and two colors in the FSYNC model (resp. the SSYNC and ASYNC models). On the other hand, we provide impossibility results for universal terminating exploration. [ABSTRACT FROM AUTHOR]