Emanuele Guido
Fusco
en
Use Knowledge to Learn Faster: Topology Recognition with Advice
https://scigraph.springernature.com/explorer/license/
chapters
chapter
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.
true
31-45
2013-01-01
2013
http://link.springer.com/10.1007/978-3-642-41527-2_3
2019-04-15T22:01
Berlin, Heidelberg
Springer Berlin Heidelberg
Département d’informatique, Université du Québec en Outaouais, Gatineau, Québec, J8X 3X7, Canada
Université du Québec en Outaouais
e742bd09cbd4db13b51ba6358775487b90d2c68d3d52d959db290d048289681e
readcube_id
Yehuda
Afek
Information and Computing Sciences
978-3-642-41526-5
978-3-642-41527-2
Distributed Computing
Springer Nature - SN SciGraph project
Rossella
Petreschi
Sapienza University of Rome
Computer Science Department, Sapienza University of Rome, 00198 Rome, Italy
dimensions_id
pub.1048545177
Pelc
Andrzej
Artificial Intelligence and Image Processing
doi
10.1007/978-3-642-41527-2_3