Distributed Computation and Reconfiguration in Actively Dynamic Networks
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In this paper, we study systems of distributed entities that can actively modify their communication network. This gives rise to distributed algorithms that apart from communication can also exploit network reconfiguration in order to carry out a given task. At the same time, the distributed task itself may now require global reconfiguration from a given initial network G_s to a target network G_f from a family of networks having some good properties, like small diameter. With reasonably powerful computational entities, there is a straightforward algorithm that transforms any G_s into a spanning clique in O(log n) time. The algorithm can then compute any global function on inputs and reconfigure to any target network in one round. We argue that such a strategy is impractical for real applications. In real dynamic networks there is a cost associated with creating and maintaining connections. To formally capture such costs, we define three edge-complexity measures: the total edge activations, the maximum activated edges per round, and the maximum activated degree of a node. The clique formation strategy highlighted above, maximizes all of them. We aim at improved algorithms that achieve (poly)log(n) time while minimizing the edge-complexity for the general task of transforming any G_s into a G_f of diameter (poly)log(n). We give three distributed algorithms. The first runs in O(log n) time, with at most 2n active edges per round, an optimal total of O(nlog n) edge activations, a maximum degree n-1, and a target network of diameter 2. The second achieves bounded degree by paying an additional logarithmic factor in time and in total edge activations and gives a target network of diameter O(log n). Our third algorithm shows that if we slightly increase the maximum degree to polylog(n) then we can achieve a running time of o(log^2 n).
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