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Lower and upper bounds for deterministic convergecast with labeling schemes

Abstract : In wireless networks, broadcast and convergecast are the two most used communication primitives. Broadcast instructs a specific sink (or root) node to send a message to each node in the network. Convergecast instructs each node in the network to send a message to the sink. Without labels, deterministic convergecast is impossible even in a three-nodes network. Therefore, networking solutions for convergecast are based on probabilistic approaches or use underlying probabilistic medium access protocols such as CSMA/CA or CSMA/CD. In this paper, we focus on deterministic convergecast algorithms enhanced with labeling schemes. We investigate two communication modes: half-duplex (nodes either transmit or receive but not both at the same time) and full-duplex (nodes can transmit and receive data at the same time). For these two modes we investigate time and labeling lower and upper bounds. Even though broadcast and convergecast are similar, we prove that, contrary to broadcast, deterministic convergecast cannot be solved with short labels for some topologies. That is, O(log(n)) bits are necessary to solve deterministically convergecast where n is the number of nodes in the network. We also prove that O(n) communication time slots is required. We provide solutions that are optimal in the worst case scenarios, in terms of labeling and communication.
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https://hal.archives-ouvertes.fr/hal-02650472
Contributor : Gewu Bu <>
Submitted on : Monday, August 10, 2020 - 12:51:52 AM
Last modification on : Wednesday, August 12, 2020 - 3:15:02 AM

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Gewu Bu, Zvi Lotker, Maria Potop-Butucaru, Mikael Rabie. Lower and upper bounds for deterministic convergecast with labeling schemes. [Research Report] Sorbonne Université. 2020. ⟨hal-02650472v2⟩

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