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中文摘要：
考虑在有 m 的无限的供应下面的项目挑选的定价 n 的问题照看了买主，其各个至多对感兴趣项目的 k。目标是与利润额 p 定价每个项目 1， p 2，， p n 以便最大化全面利润。当每个项目上的价格一定在它的边缘费用上面时，由 Balcan 和 Blum 有一个 O (k) 近似算法；即，每 p i > 0。当卖主被允许在他们的边缘费用下面定价一些项目时，我们调查上述问题。它被 Balcan 等显示出。由一些下面的项目花费了的定价，卖主能可能增加最大的利润由(木头 n ) 时间。以低价格卖刺激另外的有利出售的这些项目通常被称为损失领导人。当一些项目能在费用下面被定价时，什么样的近似保证是可完成的，是不清楚的。理解这个问题被 Balcan 和 Blum 作为一个开的问题提出。在这份报纸，我们为定价损失领导人的问题给强壮的否定结果。我们证明那假设唯一的比赛推测(UGC ) ，为有在甚至当每个顾客至多是感兴趣的在里面时，允许的费用下面的价格的条款定价没有经常的近似算法三个项目。概念上，尽管由在他们的边缘费用下面卖一些项目赚更多的钱是可能的，我们的结果显示那，那么做能是计算地难处理的。
英文摘要：
Consider the problem of pricing n items under an unlimited supply with m single minded buyers, each of which is interested in at most k of the items. The goal is to price each item with profit margin p1,p2,... ,pn so as to maximize the overall profit. There is an O（k）-approximation algorithm by Balcan and Blum when the price on each item must be above its margin cost; i.e., each pi 〉 0. We investigate the above problem when the seller is allowed to price some of the items below their margin cost. It was shown by Balcan et al. that by pricing some of the items below cost, the seller could possibly increase the maximum profit by /2（logn） times. These items sold at low prices to stimulate other profitable sales are usually called ＂loss leader＂. It is unclear what kind of approximation guarantees are achievable when some of the items can be priced below cost. Understanding this question is posed as an open problem by Balcan and Blum. In this paper, we give a strong negative result for the problem of pricing loss leaders . We prove that assuming the Unique Games Conjecture （UGC）, there is no constant approximation algorithm for item pricing with prices below cost allowed even when each customer is interested in at most three items. Conceptually, our result indicates that although it is possible to make more money by selling some items below their margin cost, it can be computationally intractable to do so.
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