?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=http%3A%2F%2Feprints.imtlucca.it%2F2116%2F&rft.title=Multicolored+dynamos+on+toroidal+meshes&rft.creator=Brunetti%2C+Sara&rft.creator=Lodi%2C+Elena&rft.creator=Quattrociocchi%2C+Walter&rft.subject=QA75+Electronic+computers.+Computer+science&rft.description=Detecting+on+a+graph+the+presence+of+the+minimum+number+of+nodes+(target+set)+that+will+be+able+to+%22activate%22+a+prescribed+number+of+vertices+in+the+graph+is+called+the+target+set+selection+problem+(TSS)+proposed+by+Kempe%2C+Kleinberg%2C+and+Tardos.+In+TSS's+settings%2C+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%2C+and+the+threshold+is+given+by+the+state+of+the+majority+of+neighbors.+Here%2C+the+major+effort+was+in+determining+the+distribution+of+initial+faults+leading+the+entire+system+to+a+faulty+behavior.+Such+an+activation+pattern%2C+also+known+as+dynamic+monopoly+(or+shortly+dynamo)%2C+was+introduced+by+Peleg+in+1996.+In+this+paper+we+extend+the+TSS+problem's+settings+by+representing+nodes'+states+with+a+%22multicolored%22+set.+The+extended+version+of+the+problem+can+be+described+as+follows%3A+let+G+be+a+simple+connected+graph+where+every+node+is+assigned+a+color+from+a+finite+ordered+set+C+%3D+%7B1%2C+.+.+.%2C+k%7D+of+colors.+At+each+local+time+step%2C+each+node+can+recolor+itself%2C+depending+on+the+local+configurations%2C+with+the+color+held+by+the+majority+of+its+neighbors.+Given+G%2C+we+study+the+initial+distributions+of+colors+leading+the+system+to+a+k+monochromatic+configuration+in+toroidal+meshes%2C+focusing+on+the+minimum+number+of+initial+k-colored+nodes.+We+find+upper+and+lower+bounds+to+the+size+of+a+dynamo%2C+and+then+special+classes+of+dynamos%2C+outlined+by+means+of+a+new+approach+based+on+recoloring+patterns%2C+are+characterized.+&rft.publisher=ArXiv&rft.date=2010&rft.type=Working+Paper&rft.type=NonPeerReviewed&rft.identifier=++Brunetti%2C+Sara+and+Lodi%2C+Elena+and+Quattrociocchi%2C+Walter++Multicolored+dynamos+on+toroidal+meshes.++Working+Paper++%23+%2F2010++++ArXiv+++++++(Submitted)+++&rft.relation=http%3A%2F%2Farxiv.org%2Fabs%2F1012.4404