OPODIS 2014: Principles of Distributed Systems pp 186-201

# Scalable Wake-up of Multi-channel Single-Hop Radio Networks

• Bogdan S. Chlebus
• Gianluca De Marco
• Dariusz R. Kowalski
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8878)

## Abstract

We consider waking up a single-hop radio network with multiple channels. There are n stations connected to b channels without collision detection. Some k stations may become active spontaneously at arbitrary times, where k is unknown, and the goal is for all the stations to hear a successful transmission as soon as possible after the first spontaneous activation. We present a deterministic algorithm for the general problem that wakes up the network in $${\mathcal O}(k\log^{1/b} k\log n)$$ time. We prove a lower bound that any deterministic algorithm requires $$\Omega(\frac{k}{b}\log \frac{n}{k})$$ time. We give a deterministic algorithm for the special case when b > d loglogn, for some constant d > 1, which wakes up the network in $${\mathcal O}(\frac{k}{b}\log n\log(b\log n))$$ time. This algorithm misses time optimality by at most a factor of lognlogb. We give a randomized algorithm that wakes up the network within $${\mathcal O}(k^{1/b}\ln \frac{1}{\epsilon})$$ rounds with the probability of at least 1 − ε, for any unknown 0 < ε < 1. We also consider a model of jamming, in which each channel in any round may be jammed to prevent a successful transmission, which happens with some known parameter probability p, independently across all channels and rounds. For this model, we give a deterministic algorithm that wakes up the network in $${\mathcal O}(\log^{-1}(1/p) k\log n\log^{1/b} k)$$ time with the probability of at least 1 − 1/poly(n).

## Keywords

multiple access channel radio network multi-channel wake-up randomized algorithms distributed algorithms

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© Springer International Publishing Switzerland 2014

## Authors and Affiliations

• Bogdan S. Chlebus
• 1
• Gianluca De Marco
• 2
• Dariusz R. Kowalski
• 3
1. 1.University of Colorado DenverDenverUSA
2. 2.Università di SalernoFiscianoItaly
3. 3.University of LiverpoolLiverpoolUnited Kingdom