Use Knowledge to Learn Faster: Topology Recognition with Advice View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2013

AUTHORS

Emanuele Guido Fusco , Andrzej Pelc , Rossella Petreschi

ABSTRACT

We investigate tradeoffs between the time in which topology recognition is accomplished and the minimum size of advice that has to be given to nodes. We provide upper and lower bounds on the minimum size of advice that is sufficient to perform topology recognition in a given time, in the class of all graphs of size n and diameter D ≤ αn, for any constant α D − k, where 0 k ≤ D, then the optimal size of advice is Θ((n 2 logn)/(D − k + 1)). If the allotted time is D, then this optimal size is Θ(n logn). If the allotted time is D + k, where 0 k ≤ D/2, then the optimal size of advice is Θ(1 + (logn) / k). The only remaining gap between our bounds is for time D + k, where D/2 k ≤ D. In this time interval our upper bound remains O(1 + (logn) / k), while the lower bound (that holds for any time) is 1. This leaves a gap if D ∈ o(logn). Finally, we show that for time 2D + 1, one bit of advice is both necessary and sufficient. Our results show how sensitive is the minimum size of advice to the time allowed for topology recognition: allowing just one round more, from D to D + 1, decreases exponentially the advice needed to accomplish this task. More... »

PAGES

31-45

References to SciGraph publications

Book

TITLE

Distributed Computing

ISBN

978-3-642-41526-5
978-3-642-41527-2

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-642-41527-2_3

DOI

http://dx.doi.org/10.1007/978-3-642-41527-2_3

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1048545177


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