Abstract
Helping user identify the ideal results of a manageable size k from a database, such that each user’s ideal results will take a big picture of the whole database. This problem has been studied extensively in recent years under various models, resulting in a large number of interesting consequences. In this paper, we introduce the concept of minimum happiness ratio maximization and show that our objective function exhibits the property of monotonictity. Based on this property, two efficient polynomial-time approximation algorithms called Lazy NWF-Greedy and Lazy Stochastic-Greedy are developed. Both of them are extended to exploit lazy evaluations, yielding significant speedups as to basic RDP-Greedy algorithm. Extensive experiments on both synthetic and real datasets show that our Lazy NWF-Greedy achieves the same minimum happiness ratio as the best-known RDP-Greedy algorithm but can greatly reduce the number of function evaluations and our Lazy Stochastic-Greedy sacrifices a little happiness ratio but significantly decreases the number of function evaluations.
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Notes
- 1.
Our minimum happiness ratio maximization is consistent with the k-regret proposed in [10]. However, k-regret denotes different things by Nanongkai et al. [10] and Chester et al. [13]. In the former, k-regret is the representative set of k objects, whereas in the latter, k-regret is used to denote the regret between the scores of top 1 and top k. To avoid confusion, we refer k-regret in [13] to kRMS.
- 2.
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Acknowledgment
This work is partially supported by the National Natural Science Foundation of China under grant Nos. U1733112,61702260, the Natural Science Foundation of Jiangsu Province of China under grant No. BK20140826, the Fundamental Research Funds for the Central Universities under grant No. NS2015095, Funding of Graduate Innovation Center in NUAA under grant No. KFJJ20171605.
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Qiu, X., Zheng, J., Dong, Q., Huang, X. (2018). Speed-Up Algorithms for Happiness-Maximizing Representative Databases. In: U, L., Xie, H. (eds) Web and Big Data. APWeb-WAIM 2018. Lecture Notes in Computer Science(), vol 11268. Springer, Cham. https://doi.org/10.1007/978-3-030-01298-4_27
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