求k-遗憾极小集的有效算法
Efficient Algorithms for k-Regret Minimizing Sets
摘要：
遗憾最小化集合Q是大得多的数据库P的小尺寸表示，使得在Q上执行的用户查询返回的答案的分数不比完整数据集上的分数差得多。特别地，k-后悔最小化集合具有Q中的前1项的得分与P中的前k项的得分之间的后悔比率最小化的性质，其中项的得分是项的属性与用户的权重（偏好）向量的内积。这个问题是具有挑战性的，因为我们想找到一个单一的代表集Q，其后悔率相对于所有可能的用户权重向量是小的。我们证明了k-后悔极小化对所有维数d>= 3是NP-完全的。这解决了Chester等人[VLDB 2014]的一个开放问题，并解决了所有d的问题的复杂性状态：已知该问题具有d <= 2的多项式时间解。此外，我们提出了两个新的近似计划的遗憾最小化，都与可证明的保证，一个基于coresets和另一个基于碰集。我们还进行了广泛的实验评估，并表明我们的计划计算遗憾最小化集的大小与[VLDB 14]中提出的贪心算法相当，但我们的计划显着更快，可扩展到大数据集。
英文摘要：
A regret minimizing set Q is a small size representation of a much larger database P so that user queries executed on Q return answers whose scores are not much worse than those on the full dataset. In particular, a k-regret minimizing set has the property that the regret ratio between the score of the top-1 item in Q and the score of the top-k item in P is minimized, where the score of an item is the inner product of the item's attributes with a user's weight (preference) vector. The problem is challenging because we want to find a single representative set Q whose regret ratio is small with respect to all possible user weight vectors. We show that k-regret minimization is NP-Complete for all dimensions d >= 3. This settles an open problem from Chester et al. [VLDB 2014], and resolves the complexity status of the problem for all d: the problem is known to have polynomial-time solution for d <= 2. In addition, we propose two new approximation schemes for regret minimization, both with provable guarantees, one based on coresets and another based on hitting sets. We also carry out extensive experimental evaluation, and show that our schemes compute regret-minimizing sets comparable in size to the greedy algorithm proposed in [VLDB 14] but our schemes are significantly faster and scalable to large data sets.
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