Latency Optimal Broadcasting in Noisy Wireless Mesh Networks

In this paper, we adopt a new noisy wireless network model introduced very recently by Censor-Hillel et al. in [ACM PODC 2017, CHHZ17]. More specifically, for a given noise parameter $p\in [0,1],$ any sender has a probability of $p$ of transmitting noise or any receiver of a single transmission in its neighborhood has a probability $p$ of receiving noise. In this paper, we first propose a new asymptotically latency-optimal approximation algorithm (under faultless model) that can complete single-message broadcasting task in $D+O(\log^2 n)$ time units/rounds in any WMN of size $n,$ and diameter $D$. We then show this diameter-linear broadcasting algorithm remains robust under the noisy wireless network model and also improves the currently best known result in CHHZ17 by a $\Theta(\log\log n)$ factor. In this paper, we also further extend our robust single-message broadcasting algorithm to $k$ multi-message broadcasting scenario and show it can broadcast $k$ messages in $O(D+k\log n+\log^2 n)$ time rounds. This new robust multi-message broadcasting scheme is not only asymptotically optimal but also answers affirmatively the problem left open in CHHZ17 on the existence of an algorithm that is robust to sender and receiver faults and can broadcast $k$ messages in $O(D+k\log n + polylog(n))$ time rounds.Comment: arXiv admin note: text overlap with arXiv:1705.07369 by other author

Faster Centralized Communication in Radio Networks

We study the communication primitives of broadcasting (one-to-all communication) and gossiping (all-to-all communication) in known topology radio networks, i.e., where for each primitive the schedule of transmissions is precomputed based on full knowledge about the size and the topology of the network. Δ log n log Δ−log log n We show that gossiping can be completed in O(D +) time units in any radio network of size n, diameter D and maximum degree Δ = Ω(log n). This is an almost optimal schedule in the sense that there exists a radio network topology, such as: a Δ-regular tree in which the radio gossiping cannot be completed in less than Ω(D + D + O ( log3 n log log n Δ log n log Δ) units of time. Moreover, we show a) schedule for the broadcast task. Both our transmission schemes significantly improve upon the currently best known schedules in G ˛asieniec, Peleg and Xin [PODC’05], i.e., a O(D + Δ log n) time schedule for gossiping and a D + O(log 3 n) time schedule for broadcast. Our broadcasting schedule also improves, for large D, a very recent O(D +log 2 n) time broadcasting schedule by Kowalski and Pelc