简介：Classicalsortingbyreversalsusestheunit-costmodel,thatis,eachreversalconsumesanequalcost.Thismodellimitsthebiologicalmeaningofsortingbyreversal.Benderandhiscolleaguesextendeditbyassigningacostfunctionf(l)=lαforallα≥0,wherelisthelengthofthereversedsubsequence.Inthispaper,weextendtheirresultsbyconsideringamodelinwhichlongreversalsareprohibited.Usingthesamecostfunctionaboveforpermittedreversals,wepresenttightornearlytightboundsfortheworst-casecostofsortingbyreversals.Thenwedevelopalgorithmstoapproximatetheoptimalcosttosortagiven0/1sequenceaswellasagivenpermutation.OurproposedproblemsaremorebiologicallymeaningfulandmorealgorithmicallygeneralandchallengingthantheproblemconsideredbyBenderetal.Furthermore,ourboundsaretightandnearlytight,whereasouralgorithmsprovidegoodapproximationratioscomparedtotheoptimalcosttosort0/1sequencesorpermutationsbyreversals.