社交网络中优惠券的最优分配：一种近似次模优化方法
Toward Optimal Coupon Allocation in Social Networks: An Approximate Submodular Optimization Approach
摘要：
CMO委员会报告说，美国71%的互联网用户在做出购买决定时受到优惠券和折扣的影响。它还表明，提供优惠券给一小部分用户（称为种子用户）可能会影响许多其他用户在社交网络中的购买决策。这促使我们研究最优优惠券分配问题，我们的目标是将优惠券分配给一组用户，以最大化预期的级联。不同于现有的研究影响最大化（IM），我们的框架允许一个通用的效用函数和一组更复杂的约束。特别是，我们制定我们的问题作为一个近似的次模最大化问题的拟阵和背包约束。现有的基于效用函数次模性的算法，如贪心算法，不能直接对非次模函数进行求解。我们使用$ε$来衡量我们的函数和它的最接近的子模函数之间的差异，并提出了一种新的近似算法与近似比$β(ε)$与$\lim_{ε\rightarrow 0}β(ε)=1-1/e$。这是最好的近似保证近似次模最大化的分区拟阵和背包约束，我们的结果适用于广泛的优化问题，可以制定为一个近似次模最大化问题。
英文摘要：
CMO Council reports that 71\% of internet users in the U.S. were influenced by coupons and discounts when making their purchase decisions. It has also been shown that offering coupons to a small fraction of users (called seed users) may affect the purchase decisions of many other users in a social network. This motivates us to study the optimal coupon allocation problem, and our objective is to allocate coupons to a set of users so as to maximize the expected cascade. Different from existing studies on influence maximizaton (IM), our framework allows a general utility function and a more complex set of constraints. In particular, we formulate our problem as an approximate submodular maximization problem subject to matroid and knapsack constraints. Existing techniques relying on the submodularity of the utility function, such as greedy algorithm, can not work directly on a non-submodular function. We use $ε$ to measure the difference between our function and its closest submodular function and propose a novel approximate algorithm with approximation ratio $β(ε)$ with $\lim_{ε\rightarrow 0}β(ε)=1-1/e$. This is the best approximation guarantee for approximate submodular maximization subject to a partition matroid and knapsack constraints, our results apply to a broad range of optimization problems that can be formulated as an approximate submodular maximization problem.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
