Abstract
A distributed computing system can be viewed as the result of the interplay between a distributed algorithm specifying the effects of a local event (e.g. reception of a message), and an adversary choosing the interleaving (schedule) of these events in the execution. In the context of large networks of mobile pairwise interacting agents (population protocols), the adversary models the mobility of the agents by choosing the successive pairs of interacting agents. For some problems, assuming that the adversary selects the schedule according to some probability distribution greatly helps to devise (almost) correct solutions. But how much randomness is really necessary? To what extent does a problem admit implementations that are robust against a "not so random" schedule? This paper takes a first step in addressing this question by borrowing the concept of Trandomness, 0 <= T <= 1, from algorithmic information theory. Roughly speaking, the value T fixes the entropy rate of the considered schedules. For instance, the case T = 1 corresponds, in a specific sense, to schedules in which the pairs of interacting agents are chosen independently and uniformly (perfect randomness). The holy grail question can then be precisely stated as determining the optimal entropy rate to solve a given problem. We first show that perfect randomness is never required. Precisely, if a finitestate algorithm solves a problem with 1randomness, then this algorithm still solves the same problem with Trandomness for some T < 1. Second, we illustrate how to compute bounds on the optimal entropy rate of a specific problem, namely the leader election problem.
BibTeX  Entry
@InProceedings{beauquier_et_al:LIPIcs:2016:6612,
author = {Joffroy Beauquier and Peva Blanchard and Janna Burman and Rachid Guerraoui},
title = {{The Benefits of Entropy in Population Protocols}},
booktitle = {19th International Conference on Principles of Distributed Systems (OPODIS 2015)},
pages = {115},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783939897989},
ISSN = {18688969},
year = {2016},
volume = {46},
editor = {Emmanuelle Anceaume and Christian Cachin and Maria PotopButucaru},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2016/6612},
URN = {urn:nbn:de:0030drops66128},
doi = {10.4230/LIPIcs.OPODIS.2015.21},
annote = {Keywords: algorithmic randomness, entropy, leader election, distributed computing, scheduler, population protocols}
}
Keywords: 

algorithmic randomness, entropy, leader election, distributed computing, scheduler, population protocols 
Seminar: 

19th International Conference on Principles of Distributed Systems (OPODIS 2015) 
Issue Date: 

2016 
Date of publication: 

29.08.2016 