Rise and Shine Efficiently! Tight Bounds for Adversarial Wake-up
Peter Robinson, Ming Ming Tan

TL;DR
This paper establishes fundamental lower bounds and proposes new algorithms for the wake-up problem in distributed networks under adversarial conditions, focusing on message complexity and advice-based strategies.
Contribution
It provides the first super-linear lower bounds for the wake-up problem without extensive topology knowledge and introduces efficient algorithms with near-optimal complexity.
Findings
Lower bounds on message complexity in advice and non-advice models.
New algorithms with $O(n \, \log n)$ and $O(\rho_{awk})$ rounds.
Deterministic advising schemes with $O(\rho_{awk} \log^2 n)$ time and $O(n \log^2 n)$ messages.
Abstract
We study the wake-up problem in distributed networks, where an adversary awakens a subset of nodes at arbitrary times, and the goal is to wake up all other nodes as quickly as possible by sending only few messages. We prove the following lower bounds: * We first consider the setting where each node receives advice from an oracle who can observe the entire network, but does not know which nodes are awake initially. More specifically, we consider the model with advice. We prove that any randomized algorithm must send messages if nodes receive only bits of advice on average. * For the assumption, we show that any -time algorithm requires messages. Our result is the first super-linear (in ) lower bound, for a problem that does not require individual nodes to learn a large amount of…
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Taxonomy
TopicsAdvanced Optical Network Technologies · Software-Defined Networks and 5G · Smart Grid Security and Resilience
