ABSTRACT
The aggregation problem assumes that every process starts an execution with a unique token (an abstraction for data). The goal is to collect these tokens at a minimum number of processes by the end of the execution. This problem is particularly relevant to mobile networks where peer-to-peer communication is cheap (e.g., using 802.11 or Bluetooth), but uploading data to a central server can be costly (e.g., using 3G/4G). With this in mind, we study this problem in a dynamic network model, in which the communication graph can change arbitrarily from round to round.
We start by exploring global bounds. First we prove a negative result that shows that in general dynamic graphs no algorithm can achieve any measure of competitiveness against the optimal offline algorithm. Guided by this impossibility result, we focus our attention to dynamic graphs where every node interacts, at some point in the execution, with at least a p-fraction of the total number of nodes in the graph. We call these graphs p-clusters. We describe a distributed algorithm that in p-clusters aggregates the tokens to O(log n) processes with high probability.
We then turn our attention to local bounds. Specifically we ask whether its possible to aggregate to O(log n) processes in parts of the graph that locally form a p-cluster. Here we prove a negative result: this is only possible if the local p-clusters are sufficiently isolated from the rest of the graph. We then match this result with an algorithm that achieves the desired aggregation given (close to) the minimal required p-cluster isolation. Together, these results imply a "paradox of connectivity": in some graphs, increasing connectivity can lead to inherently worse aggregation performance.
We conclude by considering what seems to be a promising performance metric to circumvent our lower bounds for local aggregation algorithms. However, perhaps surprisingly, we show that no aggregation algorithm can perform well with respect to this metric, even in very well connected and very well isolated clusters.
- J. Aspnes and E. Ruppert. An Introduction to Population Protocols. Bulletin of the European Association for Theoretical Computer Science, 93:98--117, 2007.Google Scholar
- K. Censor Hillel and H. Shachnai. Partial Information Spreading with Application to Distributed Maximum Coverage. In Proceedings of the International Symposium on Principles of Distributed Computing, 2010. Google ScholarDigital Library
- A. Cornejo and C. Newport. Prioritized Gossip in Vehicular Networks. In Proceedings of the International Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications, 2010. Google ScholarDigital Library
- B. Haeupler. Analyzing Network Coding Gossip Made Easy. Arxiv preprint arXiv:1010.0558, 2010.Google Scholar
- B. Hull, V. Bychkovsky, Y. Zhang, K. Chen, M. Goraczko, A. Miu, E. Shih, H. Balakrishnan, and S. Madden. CarTel: a Distributed Mobile Sensor Computing System. In Proceedings of the Conference on Embedded Networked Sensor System, 2006. Google ScholarDigital Library
- C. Intanagonwiwat, D. Estrin, R. Govindan, and J. Heidemann. Impact of Network Density on Data Aggregation in Wireless Sensor Networks. In Proceedings of the Conference on Distributed Computing Systems, 2002. Google ScholarDigital Library
- S. Janson, T. Luczak, and A. Rucinski. Random Graphs. John Wiley & Sons Inc., 2000.Google ScholarCross Ref
- L. Krishnamachari, D. Estrin, and S. Wicker. The Impact of Data Aggregation in Wireless Sensor Networks. In Proceedings of the Conference of Distributed Computing Systems, 2002. Google ScholarDigital Library
- F. Kuhn, N. Lynch, and R. Oshman. Distributed Computation in Dynamic Networks. In Proceedings of the Symposium on Theory of Computing, 2010. Google ScholarDigital Library
- F. Kuhn, Y. Moses, and R. Oshman. Coordinated Consensus in Dynamic Networks. In Proceedings of the International Symposium on Principles of Distributed Computing, 2011. Google ScholarDigital Library
- F. Kuhn and R. Oshman. Dynamic networks: models and algorithms. ACM SIGACT News, 42(1):82--96, 2011. Google ScholarDigital Library
- S. Madden, M. Franklin, J. Hellerstein, and W. Hong. Tag: a Tiny Aggregation Service for Ad-Hoc Sensor Networks. ACM SIGOPS Operating Systems Review, 36(SI):131--146, 2002. Google ScholarDigital Library
- R. Pinheiro, A. Poylisher, and H. Caldwell. Mobile Agents for Aggregation of Network Management Data. In Proceedings of the International Symposium on Mobile Agents, 1999. Google ScholarDigital Library
- A. Thiagarajan, L. Ravindranath, H. Balakrishnan, S. Madden, and L. Girod. Accurate, Low-Energy Trajectory Mapping for Mobile Devices. In Proceedings of the Symposium on Networked Systems Design and Implementation, 2011. Google ScholarDigital Library
Index Terms
- Aggregation in dynamic networks
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