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Deterministic communication in radio networks
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Czumaj, Artur and Davies, Peter (2018) Deterministic communication in radio networks. SIAM Journal on Computing, 47 (1). pp. 218-240. doi:10.1137/17M1111322
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Official URL: https://doi.org/10.1137/17M1111322
Abstract
In this paper we improve the deterministic complexity of two fundamental communication primitives in the classical model of ad hoc radio networks with unknown topology: broadcasting and wake-up. We consider an unknown radio network, in which all nodes have no prior knowledge about network topology, and know only the size of the network $n$, the maximum in-degree of any node $\Delta$, and the eccentricity of the network $D$. For such networks, we first give an algorithm for wake-up, based on the existence of small universal synchronizers. This algorithm runs in $O(\frac{\min\{n, D\Delta\} \log n \log \Delta}{\log\log \Delta})$ time, the fastest known in both directed and undirected networks, improving over the previous best $O(n \log^2n)$-time result across all ranges of parameters, but particularly when maximum in-degree is small. Next, we introduce a new combinatorial framework of block synchronizers and prove the existence of such objects of low size. Using this framework, we design a new deterministic algorithm for the fundamental problem of broadcasting, running in $O(n \log D \log\log\frac{D\Delta}{n})$ time. This is the fastest known algorithm for the problem in directed networks, improving upon the $O(n \log n \log \log n)$-time algorithm of Marco [SIAM J. Comput., 39 (2010), pp. 2162--2175] and the $O(n \log^{2}D)$-time algorithm due to Czumaj and Rytter [in Proceedings of the 44th IEEE Symposium on Foundations of Computer Science (FOCS), 2003]. It is also the first to come within a log-logarithmic factor of the $\Omega(n \log D)$ lower bound due to Clementi et al. [Theoret. Comput. Sci., 302 (2003), pp. 337--364]. Our results also have direct implications on the fastest deterministic leader election and clock synchronization algorithms in both directed and undirected radio networks, tasks which are commonly used as building blocks for more complex procedures.
| Item Type: | Journal Article | ||||||
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| Subjects: | T Technology > TK Electrical engineering. Electronics Nuclear engineering | ||||||
| Divisions: | Faculty of Science > Computer Science | ||||||
| Library of Congress Subject Headings (LCSH): | Cognitive radio networks, Electric network topology | ||||||
| Journal or Publication Title: | SIAM Journal on Computing | ||||||
| Publisher: | Society for Industrial and Applied Mathematics | ||||||
| ISSN: | 0097-5397 | ||||||
| Official Date: | 15 February 2018 | ||||||
| Dates: |
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| Volume: | 47 | ||||||
| Number: | 1 | ||||||
| Page Range: | pp. 218-240 | ||||||
| DOI: | 10.1137/17M1111322 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| RIOXX Funder/Project Grant: |
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| Version or Related Resource: | A preliminary version appeared under the title "Faster deterministic communication in radio networks". in Proceedings of the 43rd International Colloquium on Automata, Languages and Programming (ICALP 2016), Rome, Italy, July 12 - 15, 2016 | ||||||
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