In　rough　sets　theory,　attribute　reduction　is　considered　as　an　important　preprocessing　step　for　machine　learning,　pattern　recognition,　and　data　mining.　The　algorithms　of　attribute　reduction　and　attribute　core　on　rough　sets　are　main　content　of　rough　sets　theory.　Positive　region　algorithm　is　an　important　branch.　Many　positive　region　algorithms　have　been　proposed,　however　the　time　and　space　complexity　is　relatively　high.　To　overcome　this　shortcoming,　we　introduce　the　size　of　positive　region　algorithm　and　positive　region　algorithm　based　on　the　simplification　decision　table.　In　order　to　verify　the　efficiency　of　the　algorithms,　we　design　several　efficient　relative　core　algorithms.　Experiments　show　the　proposed　methods　have　lower　time　complexity　and　space　complexity.　It　is　worth　noting　that　the　improvement　becomes　more　profoundly　visible　when　dealing　with　larger　data　sets.　©　2011　IEEE.