Given a seller with k types of items and n single-minded buyers, i.e., each buyer is only interested in a particular bundle of items, to maximize the revenue, the seller must assign some amount of bundles to each buyer with respect to the buyer's accepted price. Each buyer $b_i$ is associated with a value function $v_i(\cdot )$ such that $v_i(x)$ is the accepted unit bundle price $b_i$ is willing to pay for x bundles. In this paper, we assume that bundles can be sold fractionally. The single-minded item selling problem is proved to be NP-hard. Moreover, we give an $O(\sqrt{k})$-approximation algorithm. For the online version, i.e., buyers come one by one and the decision must be made immediately on the arrival of each buyer, an $O(\sqrt{k}\cdot (\log h+\log k))$-competitive algorithm is given, where h is the highest unit item price among all buyers.

给定一个卖家有k种商品和n个专一的买家，即每个买家只对特定的商品组合感兴趣，以使收益最大化，卖家必须相对于买家的商品将一定数量的商品组合分配给每个买家接受的价格。每个买家$b_{\mathrm{一世}}$ 与值函数关联 $v_{\mathrm{一世}}（\cdot ）$ 这样 $v_{\mathrm{一世}}（X）$ 是可接受的捆绑价格 $b_{\mathrm{一世}}$愿意为x个捆绑包付款。在本文中，我们假设捆绑包可以分批出售。一心一意的物品销售问题被证明是NP难的。此外，我们给$Ø（\sqrt{ķ}）$-近似算法。对于在线版本，即买家一一出现，必须在每个买家到达时立即做出决定，$Ø（\sqrt{ķ}\cdot （\mathrm{日志}H+\mathrm{日志}ķ））$给出了竞争算法，其中h是所有购买者中最高的单价。