Distributed computation in dynamic networks
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Lynch_Distributed computation.pdf
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Author(s)
Kuhn, Fabian
Lynch, Nancy A.
Oshman, Rotem
Date Issued
2010
Journal
ACM Symposium on Theory of Computing. Proceedings...STOC
Publisher
Association for Computing Machinery
Citation
Kuhn, Fabian, Nancy Lynch, and Rotem Oshman. “Distributed Computation in Dynamic Networks.” Proceedings of the 42nd ACM Symposium on Theory of Computing - STOC ’10. Cambridge, Massachusetts, USA, 2010. 513. Copyright 2010 ACM
Version
Author's final manuscript
Abstract
In this paper we investigate distributed computation in dynamic networks in which the network topology changes from round to round. We consider a worst-case model in which the communication links for each round are chosen by an adversary, and nodes do not know who their neighbors for the current round are before they broadcast their messages. The model captures mobile networks and wireless networks, in which mobility and interference render communication unpredictable. In contrast to much of the existing work on dynamic networks, we do not assume that the network eventually stops changing; we require correctness and termination even in networks that change continually. We introduce a stability property called T -interval connectivity (for T >= 1), which stipulates that for every T consecutive rounds there exists a stable connected spanning subgraph. For T = 1 this means that the graph is connected in every round, but changes arbitrarily between rounds.
We show that in 1-interval connected graphs it is possible for nodes to determine the size of the network and compute any com- putable function of their initial inputs in O(n2) [O (n superscript 2)] rounds using messages of size O(log n + d), where d is the size of the input to a single node. Further, if the graph is T-interval connected for T > 1, the computation can be sped up by a factor of T, and any function can be computed in O(n + n2/T) [(n + n superscript 2 /T)] rounds using messages of size O(log n + d). We also give two lower bounds on the token dissemination problem, which requires the nodes to disseminate k pieces of information to all the nodes in the network.
The T-interval connected dynamic graph model is a novel model, which we believe opens new avenues for research in the theory of distributed computing in wireless, mobile and dynamic networks.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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DOI of Published Version
https://doi.org/10.1145/1806689.1806760
