It　is　generally　difficult　to　estimate　tight　lower　bounds　for　many　problems　and　algorithms.　Traditionally,　lower　bounds　are　obtained　either　by　reduction　or　by　a　direct　analysis.　In　this　paper,　a　new　idea　is　presented　for　estimating　the　lower　bounds　of　problems　and　algorithms.　In　conjunction　with　two　algorithm　design　paradigms　divide　and　conquer　and　incremental　construction,　we　can　derive　good　lower　bounds　from　the　lower　bounds　of　the　corresponding　sub-problems.　©　2010　IEEE.