In　the　last　few　decades,　profit　maximization　(PM),　which　is　mainly　considered　for　maximizing　net　profits,　i.e.,　the　difference　between　gain　and　cost,　has　been　a　prominent　issue　for　online　social　networks　(OSNs).　However,　the　output-to-input　ratio,　which　is　an　important　metric　in　economics,　is　also　worth　studying　for　OSNs.　In　this　article,　we　present　a　novel　problem　that　considers　the　PM　problem　from　the　ratio　of　gain　and　cost,　known　as　output-to-input　ratio　maximization　(OIRM).　Unfortunately,　it　is　neither　submodular　nor　supermodular.　The　hill-climbing　greedy　algorithm　for　solving　this　problem　is　a　1-e＜^＞-(1-c_g)　approximation　algorithm,　where　c_g　is　the　curvature　of　the　monotone　submodular　set　function　g.　To　speed　up　the　hill-climbing　greedy　algorithm,　we　propose　the　threshold　decrease　algorithm　and　prove　that　its　approximation　ratio　is　1-e＜^＞-(1-c_g)＜^＞2-epsilon　.　In　addition,　based　on　the　relationship　between　classical　net　PM　and　OIRM,　the　algorithms　for　solving　PM　can　also　solve　OIRM.　Finally,　we　evaluate　the　performance　of　our　algorithms　using　massive　experiments　on　real　datasets.　To　the　best　of　our　knowledge,　this　is　the　first　time　to　study　the　OIRM　in　viral　marketing.