Conference Paper

# Approximation Schemes for Broadcasting in Heterogenous Networks.

DOI: 10.1007/b99805 Conference: Approximation, Randomization, and Combinatorial Optimization, Algorithms and Techniques, 7th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2004, and 8th International Workshop on Randomization and Computation, RANDOM 2004, Cambridge, MA, USA, August 22-24, 2004, Proceedings

Source: DBLP

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**ABSTRACT:**We consider the problem of deterministic broadcasting in radio networks when the nodes have limited knowledge about the topology of the network. We show that for every deterministic broadcasting protocol there exists a network, of radius 2, for which the protocol takes at least $\Omega(\sqrt{n}) rounds for completing the broadcast. Our argument can be extended to prove a lower bound of Omega(\sqrt{nD}) rounds for broadcasting in radio networks of radius D. This resolves one of the open problems posed in [29], where in the authors proved a lower bound of $\Omega(n^{1/4}) rounds for broadcasting in constant diameter networks. We prove the new lower $\Omega(\sqrt{n})$ bound for a special family of radius 2 networks. Each network of this family consists of O(\sqrt{n}) components which are connected to each other via only the source node. At the heart of the proof is a novel simulation argument, which essentially says that any arbitrarily complicated strategy of the source node can be simulated by the nodes of the networks, if the source node just transmits partial topological knowledge about some component instead of arbitrary complicated messages. To the best of our knowledge this type of simulation argument is novel and may be useful in further improving the lower bound or may find use in other applications. Keywords: radio networks, deterministic broadcast, lower bound, advice string, simulation, selective families, limited topological knowledge.Theoretical Computer Science 01/2011; 412:3568-3578. · 0.49 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We consider deterministic radio broadcasting in radio networks whose nodes have full topological information about the network. We focus on radio networks having an underlying reachability graph planar. We show that there are reachability graphs such that it is impossible to complete broadcasting in less than 2.ecc(s,G) rounds, where ecc(s,G) is the eccentricity of a distinguished source ss of a graph GG. They provide a negative answer to the open problem stated by Manne, Wanq, and Xin in [F. Manne, S. Wanq, Q. Xin, Faster radio broadcasting in planar graphs, in: Proceedings of the 4th Annual Conference on Wireless on Demand Network Systems and Services, WONS’2007, IEEE Press, 2007, pp. 9–13] and show that it is impossible to complete the broadcasting task in D+O(1)D+O(1) rounds for each planar reachability graph. Particularly, we propose 3/2.D3/2.D lower bound with respect to the parameter DD — the diameter of a reachability graph. It is a nontrivial lower bound of time of centralized radio broadcasting in the case that an underlying reachability graph is planar. Moreover, we describe a generalized construction which can potentially improve the presented lower bound.Discrete Applied Mathematics 02/2009; 157(4):853–857. · 0.72 Impact Factor

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