On the number of rounds necessary to disseminate information
SPAA '89 Proceedings of the first annual ACM symposium on Parallel algorithms and architectures
A lower bound for radio broadcast
Journal of Computer and System Sciences
Broadcasting in radio networks
Handbook of wireless networks and mobile computing
The Complexity of Broadcasting in Planar and Decomposable Graphs
WG '94 Proceedings of the 20th International Workshop on Graph-Theoretic Concepts in Computer Science
Centralized broadcast in multihop radio networks
Journal of Algorithms
Improved schedule for radio broadcast
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Faster communication in known topology radio networks
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
Centralized asynchronous broadcast in radio networks
Theoretical Computer Science
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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 s of a graph G. 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) rounds for each planar reachability graph. Particularly, we propose 3/2.D lower bound with respect to the parameter D - 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.