Abstract
Although any problem in a radio network can be solved using broadcast algorithms, some problems can be solved substantially more efficiently by more specialized algorithms. This paper presents two new approximate algorithms for the local sum problem, in which each node computes a (1±ε)-approximation to the sum of the values held by its incoming neighbors (nodes that have outgoing edges to the node). We propose algorithms both with and without collision detection, as well as for the beeping model, with round complexity \(O({\log^{2} n + \log n\log m \over \epsilon^2})\), where n is the number of nodes and the value held by each node is a real number in {0} ∪ [1,m]. We then show how these algorithms can be used as building blocks to construct applications such as approximate random walk distribution, PageRank, and global sum.
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References
Afek, Y., Alon, N., Bar-Joseph, Z., Cornejo, A., Haeupler, B., Kuhn, F.: Beeping a maximal independent set. In: Peleg, D. (ed.) DISC 2011. LNCS, vol. 6950, pp. 32–50. Springer, Heidelberg (2011)
Avrachenkov, K., Litvak, N., Nemirovsky, D., Osipova, N.: Monte carlo methods in pagerank computation: When one iteration is sufficient. SIAM J. Numer. Anal. 45(2), 890–904 (2007)
Bar-Yehuda, R., Goldreich, O., Itai, A.: On the time-complexity of broadcast in radio networks: An exponential gap between determinism randomization. In: Proceedings of the Sixth Annual ACM Symposium on Principles of Distributed Computing, PODC 1987, pp. 98–108. ACM, New York (1987)
Capetanakis, J.: Generalized tdma: The multi-accessing tree protocol. IEEE Transactions on Communications 27(10), 1476–1484 (1979)
Capetanakis, J.: Tree algorithms for packet broadcast channels. IEEE Trans. Inf. Theor. 25(5), 505–515 (2006)
Chlamtac, I., Kutten, S.: On broadcasting in radio networks–problem analysis and protocol design. IEEE Transactions on Communications 33(12), 1240–1246 (1985)
Cornejo, A., Kuhn, F.: Deploying wireless networks with beeps. In: Lynch, N.A., Shvartsman, A.A. (eds.) DISC 2010. LNCS, vol. 6343, pp. 148–162. Springer, Heidelberg (2010)
Czumaj, A., Rytter, W.: Broadcasting algorithms in radio networks with unknown topology. In: Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science, pp. 492–501 (2003)
Gasieniec, L., Peleg, D., Xin, Q.: Faster communication in known topology radio networks. In: Proceedings of the Twenty-fourth Annual ACM Symposium on Principles of Distributed Computing, PODC 2005, pp. 129–137. ACM, New York (2005)
Gąsieniec, L., Pelc, A., Peleg, D.: The wakeup problem in synchronous broadcast systems (extended abstract). In: Proceedings of the Nineteenth Annual ACM Symposium on Principles of Distributed Computing, PODC 2000, pp. 113–121. ACM, New York (2000)
Ghaffari, M., Haeupler, B., Khabbazian, M.: Randomized broadcast in radio networks with collision detection. In: Proceedings of the 2013 ACM Symposium on Principles of Distributed Computing, PODC 2013, pp. 325–334. ACM, New York (2013)
Ghaffari, M., Haeupler, B., Lynch, N., Newport, C.: Bounds on contention management in radio networks. In: Aguilera, M.K. (ed.) DISC 2012. LNCS, vol. 7611, pp. 223–237. Springer, Heidelberg (2012)
Greenberg, A.G., Flajolet, P., Ladner, R.E.: Estimating the multiplicities of conflicts to speed their resolution in multiple access channels. J. ACM 34(2), 289–325 (1987)
Hayes, J.F.: An adaptive technique for local distribution. IEEE Transactions on Communications 26(8), 1178–1186 (1978)
Huang, B., Moscibroda, T.: Conflict resolution and membership problem in beeping channels. In: Afek, Y. (ed.) DISC 2013. LNCS, vol. 8205, pp. 314–328. Springer, Heidelberg (2013)
Jurdziński, T., Stachowiak, G.: Probabilistic algorithms for the wakeup problem in single-hop radio networks. In: Bose, P., Morin, P. (eds.) ISAAC 2002. LNCS, vol. 2518, pp. 535–549. Springer, Heidelberg (2002)
Kowalski, D.R., Pelc, A.: Broadcasting in undirected ad hoc radio networks. In: Proceedings of the Twenty-second Annual Symposium on Principles of Distributed Computing, PODC 2003, pp. 73–82. ACM, New York (2003)
Mitzenmacher, M., Upfal, E.: Probability and computing - randomized algorithms and probabilistic analysis. Cambridge University Press (2005)
Page, L., Brin, S., Motwani, R., Winograd, T.: The pagerank citation ranking: Bringing order to the web. Technical report. Stanford University (1999)
Das Sarma, A., Molla, A.R., Pandurangan, G., Upfal, E.: Fast distributed pagerank computation. In: Frey, D., Raynal, M., Sarkar, S., Shyamasundar, R.K., Sinha, P. (eds.) ICDCN 2013. LNCS, vol. 7730, pp. 11–26. Springer, Heidelberg (2013)
Tsybakov, B.S., Mikhailov, V.A.: Free synchronous access of packets to a broadcast feedback channel. Problems Inform. Transmission 14(4), 259–280 (1978)
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Liu, Z., Herlihy, M. (2014). Approximate Local Sums and Their Applications in Radio Networks. In: Kuhn, F. (eds) Distributed Computing. DISC 2014. Lecture Notes in Computer Science, vol 8784. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45174-8_17
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DOI: https://doi.org/10.1007/978-3-662-45174-8_17
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