eprintid: 2116
rev_number: 10
eprint_status: archive
userid: 6
dir: disk0/00/00/21/16
datestamp: 2014-01-24 11:48:20
lastmod: 2014-01-24 13:10:57
status_changed: 2014-01-24 11:48:20
type: monograph
metadata_visibility: show
creators_name: Brunetti, Sara
creators_name: Lodi, Elena
creators_name: Quattrociocchi, Walter
creators_id: 
creators_id: 
creators_id: walter.quattrociocchi@imtlucca.it
title: Multicolored dynamos on toroidal meshes
ispublished: submitted
subjects: QA75
divisions: CSA
full_text_status: none
monograph_type: working_paper
keywords: Distributed, Parallel, and Cluster Computing (cs.DC); Computational Complexity (cs.CC); Data Structures and Algorithms (cs.DS); Social and Information Networks (cs.SI)
abstract: Detecting on a graph the presence of the minimum number of nodes (target set) that will be able to "activate" a prescribed number of vertices in the graph is called the target set selection problem (TSS) proposed by Kempe, Kleinberg, and Tardos. In TSS's settings, nodes have two possible states (active or non-active) and the threshold triggering the activation of a node is given by the number of its active neighbors. Dealing with fault tolerance in a majority based system the two possible states are used to denote faulty or non-faulty nodes, and the threshold is given by the state of the majority of neighbors. Here, the major effort was in determining the distribution of initial faults leading the entire system to a faulty behavior. Such an activation pattern, also known as dynamic monopoly (or shortly dynamo), was introduced by Peleg in 1996. In this paper we extend the TSS problem's settings by representing nodes' states with a "multicolored" set. The extended version of the problem can be described as follows: let G be a simple connected graph where every node is assigned a color from a finite ordered set C = {1, . . ., k} of colors. At each local time step, each node can recolor itself, depending on the local configurations, with the color held by the majority of its neighbors. Given G, we study the initial distributions of colors leading the system to a k monochromatic configuration in toroidal meshes, focusing on the minimum number of initial k-colored nodes. We find upper and lower bounds to the size of a dynamo, and then special classes of dynamos, outlined by means of a new approach based on recoloring patterns, are characterized. 
date: 2010
date_type: published
number:  
publisher: ArXiv
pages: 14
institution: IMT Institute for Advanced Studies Lucca
official_url: http://arxiv.org/abs/1012.4404
related_url_url: http://arxiv.org/pdf/1012.4404v1
citation:   Brunetti, Sara and Lodi, Elena and Quattrociocchi, Walter  Multicolored dynamos on toroidal meshes.  Working Paper  # /2010    ArXiv       (Submitted)