简介：

简介：Hausdorffdistancebetweentwocompactsets,definedasthemaximumdistancefromapointofonesettoanotherset,hasmanyapplicationincomputerscience.Itisagoodmeasureforthesimilarityoftwosets.ThispaperprovesthattheshapedistancebetweentwocompactsetsinR~ndefinedbyminimumHausdorffdistanceunderrigidmotionsisadistance.Theauthorsintroducesimilaritycomparisonproblemsinproteinscience,andproposethatthismeasuremayhavegoodapplicationtocomparisonofproteinstructureaswell.Forcalculationofthisdistance,theauthorsgiveonedimensionalformulasforproblems(2,n),(3,3),and(3,4).Theseformulascanreducetimeneededforsolvingtheseproblems.Theauthorsdidsomenumericalexperimentsfor(2,n).Onthesesetsofdata,thisformulacanreducetimeneededtoonefifteenthofthebestalgorithmsknownonaverage.Asnincreases,itwouldsavemoretime.