Abstract. A data cube is a popular organization for summary data. A cube is simply a multidimensional structure that contains in each cell an aggregate value, i.e., the result of applying an aggregate function to an underlying relation. In practical situat

270´ANDWUBARBARA

theanswersexhibitsanerrorthatgoesbeyond3%,inspiteofthe40%errorthattheindividualcellsinthecuboidmayreach.

Figure5showstheresultsofrunningqueriestocomputeeachoneofthecuboidsinthelatticeofthedatacube(withtheexception,ofcourse,ofthecorecuboid,whichwehaveinthecompressedform).Thequeriesarerunoverthecompactrepresentationofthecorecuboid.Inthetableresultsaregivenfortheminimumerroroverallthecells(minerr),themaximumerror(maxerr),theaverageerror(avgerr),thesizeofthecuboidincells(size),andahistogramthatshowsthenumberofcellsthatfallbetween0and10%oferror(0–0.1),morethan10%butlessthanorequalto20%oferror(0.1–0.2),morethan20%butlessthanorequalto30%(0.2–0.3)andmorethan30%butlessthanorequalto40%oferror(0.3–0.4).Asshown,asweaggregatemoreandmorecellstocomputethecuboidsthatareinthelowerpartofthelattice,mostoftheerrorsfallinthe rstbinofthehistogramandboththeaverageandmaximumerrorsdecreaserapidly.(Keepinmindthattheindividualcellsofthecorecuboidwerelefttohaveestimationerrorsupto40%oftherealvalue.)Figure5provesthepointwemadeintheintroduction:ifonewantstokeeperrorsinanyofthecellsofthecuboidsinthelattice(withtheexceptionofthecorecuboid)

underFigure5.Errorsforthecellsofthelatticecuboidsusingthecensusdataset.Themaximumerrorinthebasecuboidisβ=0.4.Thecolumns0–0.1,0.1–0.2,0.2–0.3and0.3–0.4containthenumberofcellsineachofthecuboidswhoseestimatederrorsarewithintheindicatedbounds:retainingcellswithhighererrorboundsmakestheerrorboundforqueriesinthatcuboidtobewithintheindicatedrange.(Forinstance,retainingallthecellsinthecolumns0.1–0.2,0.2–0.3and0.3–0.4makestheerrorforanyqueryintheallthecuboidsshownlessthan10%.