Title: Latency Optimal Broadcasting in Noisy Wireless Mesh Networks,
Abstract: 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.