A lower bound for radio broadcast
Journal of Computer and System Sciences
Journal of Computer and System Sciences
Randomized algorithms
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MobiCom '97 Proceedings of the 3rd annual ACM/IEEE international conference on Mobile computing and networking
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SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
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APPROX '01/RANDOM '01 Proceedings of the 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems and 5th International Workshop on Randomization and Approximation Techniques in Computer Science: Approximation, Randomization and Combinatorial Optimization
Deterministic Superimposed Coding with Applications to Pattern Matching
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
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FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
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ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Deterministic Communication in Radio Networks with Large Labels
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Broadcast and gossiping algorithms for mobile ad hoc networks based on breadth-first traversal
IWDC'04 Proceedings of the 6th international conference on Distributed Computing
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We study the completion time of broadcast operations on Static Ad-Hoc Wireless Networks in presence of unpredictable and dynamical faults. As for oblivious fault-tolerant distributed protocols, we provide an Ω(Dn) lower bound where n is the number of nodes of the network and D is the source eccentricity in the fault-free part of the network. Rather surprisingly, this lower bound implies that the simple Round-Robin protocol, working in O(Dn) time, is an optimal fault-tolerant oblivious protocol. Then, we demonstrate that networks of o(n/ log n) maximum in-degree admit faster oblivious protocols. Indeed, we derive an oblivious protocol having O(Dmin{n, Δ log n}) completion time on any network of maximum in-degree Δ. Finally, we address the question whether adaptive protocols can be faster than oblivious ones. We show that the answer is negative at least in the general setting: we indeed prove an Ω(Dn) lower bound when D = Θ(√n). This clearly implies that no (adaptive) protocol can achieve, in general, o(Dn) completion time.