05 July 2017, 10:30 Salle/Bat : 465/PCRI-N
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Activités de recherche : Distributed algorithms

Résumé :

Suppose to function correctly, a chemical system requires a single molecule of a certain species L. Preparing a solution with just a single copy of L is a difficult task to achieve with imprecise pipettors. Could we engineer artificial reactions (a chemical election algorithm, so to speak) that whittle down an initially large count of L to 1? Yes, with the reaction L+L→L+F: whenever two candidate leaders encounter each other, one drops out of the race. In volume v convergence to a single L requires expected time proportional to v; the final reaction --- two lone L's seeking each other in the vast expanse of volume v --- dominates the whole expected time.

One might hope that more cleverly designed reactions could elect a leader more quickly. We dash this hope: L+L→L+F, despite its sloth, is the fastest chemical algorithm for leader election there is (subject to some reasonable constraints on the reactions). The techniques generalize to establish lower bounds on the time required to do other distributed computing tasks, such as computing which of two species X or Y holds an initial majority, whether the initial number of X's is odd, or cutting the total number of X's in half.