Abstract
We study information gathering in ad-hoc radio networks. Initially, each node of the network has a piece of information called a rumor, and the overall objective is to gather all these rumors in the designated target node. The ad-hoc property refers to the fact that the topology of the network is unknown when the computation starts. Aggregation of rumors is not allowed, which means that each node may transmit at most one rumor in one step.
We focus on networks with tree topologies, that is we assume that the network is a tree with all edges directed towards the root, but, being ad-hoc, its actual topology is not known. We provide two deterministic algorithms for this problem. For the model that does not assume any collision detection nor acknowledgement mechanisms, we give an \(O(n\log \log n)\)-time algorithm, improving the previous upper bound of \(O(n\log n)\). We also show that this running time can be further reduced to O(n) if the model allows for acknowledgements of successful transmissions.
Research supported by NSF grants CCF-1217314, CCF-1536026, and NSA grant H98230-13-1-0228.
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References
Alon, N., Bar-Noy, A., Linial, N., Peleg, D.: A lower bound for radio broadcast. J. Comput. Syst. Sci. 43(2), 290–298 (1991)
Anta, A.F., Mosteiro, M.A., Munoz, J.R.: Unbounded contention resolution in multiple-access channels. Algorithmica 67(3), 295–314 (2013)
Bruschi, D., Del Pinto, M.: Lower bounds for the broadcast problem in mobile radio networks. Distrib. Comput. 10(3), 129–135 (1997)
Chlebus, B.S., Gasieniec, L., Gibbons, A., Pelc, A., Rytter, W.: Deterministic broadcasting in ad hoc radio networks. Distrib. Comput. 15(1), 27–38 (2002)
Christersson, M., Gasieniec, L., Lingas, A.: Gossiping with bounded size messages in ad hoc radio networks. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380, pp. 377–389. Springer, Heidelberg (2002)
Chrobak, M., Costello, K.: Faster information gathering in ad-hoc radio tree networks (2015). arXiv: 1512.02179
Chrobak, M., Costello, K., Gasieniec, L., Kowalski, D.R.: Information gathering in ad-hoc radio networks with tree topology. In: Zhang, Z., Wu, L., Xu, W., Du, D.-Z. (eds.) COCOA 2014. LNCS, vol. 8881, pp. 129–145. Springer, Heidelberg (2014)
Chrobak, M., Gasieniec, L., Rytter, W.: Fast broadcasting and gossiping in radio networks. J. Algorithms 43(2), 177–189 (2002)
Chrobak, M., Gasieniec, L., Rytter, W.: A randomized algorithm for gossiping in radio networks. Networks 43(2), 119–124 (2004)
Clementi, A.E.F., Monti, A., Silvestri, R.: Distributed broadcast in radio networks of unknown topology. Theor. Comput. Sci. 302(1–3), 337–364 (2003)
Czumaj, A., Rytter, W.: Broadcasting algorithms in radio networks with unknown topology. J. Algorithms 60(2), 115–143 (2006)
Erdős, P., Frankl, P., Füredi, Z.: Families of finite sets in which no set is covered by the union of \(r\) others. Israel J. Math. 51(1–2), 79–89 (1985)
Gasieniec, L.: On efficient gossiping in radio networks. In: Kutten, S., Žerovnik, J. (eds.) SIROCCO 2009. LNCS, vol. 5869, pp. 2–14. Springer, Heidelberg (2010)
Gasieniec, L., Radzik, T., Xin, Q.: Faster deterministic gossiping in directed ad hoc radio networks. In: Hagerup, T., Katajainen, J. (eds.) SWAT 2004. LNCS, vol. 3111, pp. 397–407. Springer, Heidelberg (2004)
Kowalski, D.R.: On selection problem in radio networks. In: Proceedings of the Twenty-fourth Annual ACM Symposium on Principles of Distributed Computing, PODC 2005, pp. 158–166 (2005)
Kowalski, D.R., Pelc, A.: Faster deterministic broadcasting in ad hoc radio networks. SIAM J. Discrete Math. 18(2), 332–346 (2004)
Kushilevitz, E., Mansour, Y.: An \(\varOmega (D\log (N/D))\) lower bound for broadcast in radio networks. SIAM J. Comput. 27(3), 702–712 (1998)
Liu, D., Prabhakaran, M.: On randomized broadcasting and gossiping in radio networks. In: Ibarra, O.H., Zhang, L. (eds.) COCOON 2002. LNCS, vol. 2387, pp. 340–349. Springer, Heidelberg (2002)
De Marco, G.: Distributed broadcast in unknown radio networks. In: Proceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2008), pp. 208–217 (2008)
De Marco, G., Kowalski, D.R.: Fast nonadaptive deterministic algorithm for conflict resolution in a dynamic multiple-access channel. SIAM J. Comput. 44(3), 868–888 (2015)
De Marco, G., Kowalski, D.R.: Contention resolution in a non-synchronized multiple access channel. In: IEEE 27th International Symposium on Parallel Distributed Processing (IPDPS), pp. 525–533 (2013)
Strahler, A.N.: Hypsometric (area-altitude) analysis of erosional topology. Bull. Geol. Soc. Amer. 63, 1117–1142 (1952)
Viennot, X.G.: A Strahler bijection between Dyck paths and planar trees. Discrete Math. 246, 317–329 (2003)
Xu, Y.: An \(O(n^{1.5})\) deterministic gossiping algorithm for radio networks. Algorithmica 36(1), 93–96 (2003)
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We thank the anonymous reviewers for constructive comments that helped us improve the presentation.
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Chrobak, M., Costello, K.P. (2016). Faster Information Gathering in Ad-Hoc Radio Tree Networks. In: Kranakis, E., Navarro, G., Chávez, E. (eds) LATIN 2016: Theoretical Informatics. LATIN 2016. Lecture Notes in Computer Science(), vol 9644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49529-2_21
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