Logic basedmethodsforSNPstaggingandreconstruction

SNPsarepositionsoftheDNAsequenceswherethedifferencesamongindividualsareembedded.The knowledgeofsuchSNPsiscrucialfordiseaseassociationstudies,butevenifthenumberofsuch positionsislow(about1%oftheentiresequence),thecosttoextractthecompleteinformationis actuallyveryhigh.RecentstudieshaveshownthatDNAsequencesarestructuredintoblocksof positions,thatareconservedduringevolution,wherethereisstrongcorrelationamongvalues(alleles) of differentloci.ToreducethecostofextractingSNPsinformation,theblockstructureoftheDNAhas suggestedtolimittheprocesstoasubsetofSNPs,theso-calledTagSNPs,thatareabletomaintainthe mostoftheinformationcontainedinthewholesequence.Inthispaper,weapplyatechniquefor featureselectionbasedonintegerprogrammingtotheproblemofTagSNPselection.Moreover,totest the qualityofourapproach,weconsideralsotheproblemofSNPsreconstruction,i.e.theproblemof derivingunknownSNPsfromthevalueofTagSNPsandproposetworeconstructionmethods,onebased on amajorityvoteandtheotheronamachinelearningapproach.Wetestouralgorithmontwopublic data setsofdifferentnature,providingresultsthatare,whencomparable,inlinewiththerelated literature.Oneoftheinterestingaspectsoftheproposedmethodistobefoundinitscapabilitytodeal simultaneouslywithverylargeSNPssets,and,inaddition,toprovidehighlyinformativereconstruction rules intheformoflogicformulas.