Randomized Algorithms for Determining the Majority on Graphs

Authors:
Gianluca De Marco;Andrzej Pelc
Affiliations:
Istituto di Informatica e Telematica, Consiglio Nazionale delle Ricerche, via Moruzzi 1, 56124 Pisa, Italy (e-mail: gianluca.demarco@iit.cnr.it);Département d'informatique, Université du Québec en Outaouais, Gatineau, Québec J8X 3X7, Canada (e-mail: andrzej.pelc@uqo.ca)
Venue:
Combinatorics, Probability and Computing
Year:
2006

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Abstract

Every node of an undirected connected graph is coloured white or black. Adjacent nodes can be compared and the outcome of each comparison is either 0 (same colour) or 1 (different colours). The aim is to discover a node of the majority colour, or to conclude that there is the same number of black and white nodes. We consider randomized algorithms for this task and establish upper and lower bounds on their expected running time. Our main contribution are lower bounds showing that some simple and natural algorithms for this problem cannot be improved in general.