Min-max　disagreements　are　an　important　generalization　of　the　correlation　clustering　problem　(CorCP).　It　can　be　defined　as　follows.　Given　a　marked　complete　graph　G=(V,　E),　each　edge　in　the　graph　is　marked　by　a　positive　label　＇+＇　or　a　negative　label　＇-＇　based　on　the　similarity　of　the　connected　vertices.　The　goal　is　to　find　a　clustering　C　of　vertices　V,　so　as　to　minimize　the　number　of　disagreements　at　the　vertex　with　the　most　disagreements.　Here,　the　disagreements　are　the　positive　cut　edges　and　the　negative　non-cut　edges　produced　by　clustering　C.　This　paper　considers　two　robust　min-max　disagreements:　min-max　disagreements　with　outliers　and　min-max　disagreements　with　penalties.　Given　parameter　δ\in(0,1/14),　we　first　provide　a　threshold-based　iterative　clustering　algorithm　based　on　LP-rounding　technique,　which　is　a　(1/δ,　7/(1-14δ))-bi-criteria　approximation　algorithm　for　both　the　min-max　disagreements　with　outliers　and　the　min-max　disagreements　with　outliers　on　one-sided　complete　bipartite　graphs.　Next,　we　verify　that　the　above　algorithm　can　achieve　an　approximation　ratio　of　21　for　min-max　disagreements　with　penalties　when　we　set　parameter　δ=1/21.　©　1996-2012　Tsinghua　University　Press.