We　investigate　the　problem　of　maximizing　the　sum　of　submodular　and　supermodular　functions　under　a　fairness　constraint.　This　sum　function　is　non-submodular　in　general.　For　an　offline　model,　we　introduce　two　approximation　algorithms:　A　greedy　algorithm　and　a　threshold　greedy　algorithm.　For　a　streaming　model,　we　propose　a　one-pass　streaming　algorithm.　We　also　analyze　the　approximation　ratios　of　these　algorithms,　which　all　depend　on　the　total　curvature　of　the　supermodular　function.　The　total　curvature　is　computable　in　polynomial　time　and　widely　utilized　in　the　literature.　©　1996-2012　Tsinghua　University　Press.