Abstract
In the DO-ALL problem, a set of t tasks must be performed by using a synchronous network of p processors. Processors may fail by permanent crashing. We investigate the time and the work complexity of F-reliable protocols for the DO-ALL problem on 1-hop wireless networks without collision detection. An F-reliable protocol is a protocol that guarantees the execution of all tasks if at most F < p faults happen during its execution. Previous results for this model are known only for the case F = p - 1.
We obtain the following tight bounds.
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- The completion time of F-reliable protocols on 1-hop wireless networks without collision detection is
$$ \Theta \left( {\frac{t} {{p - F}} + min\left\{ {\frac{{tF}} {p},F + \sqrt t } \right\}} \right). $$ -
- The work complexity of F-reliable protocols on 1-hop wireless networks without collision detection is
$$ \Theta \left( {t + F \cdot min\left\{ {t,F} \right\}} \right). $$
The two lower bounds hold even when the faults only happen at the very beginning of the protocol execution.
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Clementi, A.E.F., Monti, A., Silvestri, R. (2002). Optimal F-Reliable Protocols for the Do-All Problem on Single-Hop Wireless Networks. In: Bose, P., Morin, P. (eds) Algorithms and Computation. ISAAC 2002. Lecture Notes in Computer Science, vol 2518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36136-7_29
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DOI: https://doi.org/10.1007/3-540-36136-7_29
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