Abstract
In this article, we study the problem of distributed selection from a theoretical point of view. Given a general connected graph of diameter D consisting of n nodes in which each node holds a numeric element, the goal of a k-selection algorithm is to determine the kth smallest of these elements. We prove that distributed selection indeed requires more work than other aggregation functions such as, e.g., the computation of the average or the maximum of all elements. On the other hand, we show that the kth smallest element can be computed efficiently by providing both a randomized and a deterministic k-selection algorithm, dispelling the misconception that solving distributed selection through in-network aggregation is infeasible.
- Blum, M., Floyd, R. W., Pratt, V, Rivest, R. L, and Tarjan, R. E. Time bounds for selection. Journal of Computer and System Sciences. 7:448--461, 1973.Google ScholarDigital Library
- Burri, N., von Rickenbach, P., and Wattenhofer, R. Dozer. Ultra-low power data gathering in sensor networks. In International Conference on Information Processing in Sensor Networks (IPSN), 2007 Google ScholarDigital Library
- Chin, F. Y. L. and Ting, H. F. An improved algorithm for finding the median distributively. Algorithmica. 2:77--86, 1987.Google ScholarDigital Library
- Frederickson, G. N. Tradeoffs for selection in distributed networks. In Proceedings of the 2nd Annual ACM Symposium on Principles of Distributed Computing (PODC), pp. 154--160, 1983. Google ScholarDigital Library
- Goel, A. and Estrin, D. Simultaneous optimization for concave costs: Single sink aggregation or single source buy-at-bulk. Algorithmica, 43(l-2):5--15, 2005.Google Scholar
- Jia, L, Lin, G., Noubir, G., Rajaraman, R. and Sundaram, R. Universal approximations for TSP, Steiner Tree, and set cover. In 37th Annual ACM Symposium on Theory of Computing (STOC), pp. 386--395, 2005. Google ScholarDigital Library
- Kempe, D., Dobra, A., and Gehrke, J. Gossip-based computation of aggregate information. In Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science (FOCS), 2003. Google ScholarDigital Library
- Madden, S., Franklin, M. J., Hellerstein, J. M., and Hong, W. TAG: a tiny aggregation service for ad-hoc sensor networks. In Proceedings of the 5th Annual Symposium on Operating Systems Design and Implementation (OSDI), pp. 131--146,2002. Google ScholarDigital Library
- Marberg, J. M. and Gafini, E. An optimal shout-echo algorithm for selection in distributed sets. In Proceedings of the 23rd Allerton Conference on Communication, Control, and Computing, 1985.Google Scholar
- Moscibroda, T. The worst-case capacity of wireless sensor networks. In 6th International Conference on Information Processing in Sensor Networks (IPSN), 2007. Google ScholarDigital Library
- Moscibroda, T. and Wattenhofer, R. The complexity of connectivity in wireless networks. In 25th Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM), 2006.Google ScholarCross Ref
- Negro, A., Santoro, N., and Urrutia, J. Efficient distributed selection with bounded messages. IEEE Transactions of Parallel and Distributed Systems. 8(4):397--401,1997. Google ScholarDigital Library
- Patt-Shamir, B. A note on efficient aggregate queries in sensor networks. In Proceedings of the 23rd Annual ACM Symposium on Principles of Distributed Computing (PODC), pp. 283--289,2004. Google ScholarDigital Library
- Peleg, D. Distributed Computing: A Locality-Sensitive Approach. SIAM Monographs on Discrete Mathematics and Applications, 2000. Google ScholarDigital Library
- Rodeh, M. Finding the median distributively. Journal of Computer and System Science, 24(2):162--166. 1982.Google ScholarCross Ref
- Rodem, D., Santoro, N., and Sidney, J. Shout-echo selection in distributed files. Networks. 16:235--249, 1986.Google Scholar
- Santoro, N., Scheutzow, M., and Sidney, J. B. On the expected complexity of distributed selection. Journal on Parallel and Distributed Computing, 5(2):194--203, 1988. Google ScholarDigital Library
- Santoro, N., Sidney, J. B., and Sidney, S. J. A distributed selection algorithm and its expected communication complexity. Theoretical Computer Science. 100(1):185--204, 1992. Google ScholarDigital Library
- Schönhage, A., Paterson, M. S., and Pippenger, N. Finding the median. Journal of Computer and System Sciences, 13:184--199, 1976.Google ScholarDigital Library
- Shrira, L, Francez, N., and Rodeh. M. Distributed k-selection: From a sequential to a distributed algorithm. In Proceedings of the 2nd Annual ACM Symposium on Principles of Distributed Computing (PODC), pp. 143--153, 1983. Google ScholarDigital Library
- Tiwari, P. Lower bounds on communication complexity in distributed computer networks. Journal of the ACM (JACM). 34(4):921,1987. Google ScholarDigital Library
- Yao, A. Some complexity questions related to distributive computing. In Proceedings of the Annual ACM Symposium on Theory of Computing (STOC), pp. 209,1979. Google ScholarDigital Library
- Yao, Y and Gehrke, J. The Cougar approach to in-network query processing in sensor networks. ACM SIGMOD Record, 31(3):9--18, 2002. Google ScholarDigital Library
- Zhao, J., Govindan, R., and Estrin, D. Computing aggregates for monitoring wireless sensor networks. In Proceedings of the 1st IEEE International Workshop on Sensor Network Protocols and Applications (SNPA), 2003.Google ScholarCross Ref
Index Terms
- Distributed selection: a missing piece of data aggregation
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