Influence　maximization　problem　has　been　studied　extensively　with　the　development　of　online　social　networks.　Most　of　the　existing　works　focus　on　the　maximization　of　influence　spread　under　the　assumption　that　the　number　of　influenced　users　determines　the　success　of　a　product　promotion.　However,　the　profit　of　some　products　such　as　online　game　depends　on　the　interactions　among　users　besides　the　number　of　users.　In　this　paper,　we　take　both　the　number　of　active　users　and　the　user-to-user　interactions　into　account　and　propose　the　interaction-aware　influence　maximization　problem.　To　address　this　practical　issue,　we　analyze　its　complexity　and　modularity,　propose　the　sandwich　theory　which　is　based　on　decomposing　the　non-submodular　objective　function　into　the　difference　of　two　submodular　functions　and　design　two　iterated　sandwich　algorithms　which　are　guaranteed　to　get　data　dependent　approximation　solution.　Through　real　data　sets,　we　verify　the　effectiveness　of　our　proposed　algorithms.　(C)　2020　Elsevier　B.V.　All　rights　reserved.