Computing k-regret minimizing sets

Chester, Sean; Thomo, Alex; Srinivasan, Venkatesh; Whitesides, Sue

doi:10.14778/2732269.2732275

Cited by 56 publications

(105 citation statements)

References 26 publications

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“…Nanongkai et al [17] suggested the 1-regret minimizing set approach: users can have different preference functions, but, for a given tolerance of x%, it is desired to compute a subset of objects such that for every user, at least one of the subset is within x% of her top choice. This was generalized later to the k regret minimizing set [11], where the preference scores of the users top-k choice, is compared with the best in the subset. Following the definition of k-regret minimizing set in [11], we propose faster approximation algorithms for finding small representative sets.…”

Section: Introductionmentioning

confidence: 99%

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Faster Approximation Algorithm for the k-Regret Minimizing Set and Related Problems

Kumar

Sintos

2018

2018 Proceedings of the Twentieth Workshop on Algorithm Engineering and Experiments (ALENEX)

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Efficient multi-criteria decision making often requires looking at a small set of representative objects from a large collection. A recently proposed method for finding representative objects is the k-regret minimizing set (k-RMS problem). Intuitively, given a large set of objects (points) in d dimensions, the goal is to choose a small representative subset, such that for every user preference, there is always an object in the subset whose preference score is not much worse than the score of the k-th most preferred object in the original set. We propose two new efficient approximation algorithms for the k-regret minimizing set problem with provable theoretical guarantees. Our algorithms improve on the space and time complexities of previous approximation algorithms for the k-RMS problem. In addition, we run extensive experiments on real and synthetic data sets showing that simple modifications of our theoretical algorithms run significantly faster than the previous implementations of the k-RMS problem. Finally, we present an efficient approximation algorithm with theoretical guarantees for an extension of the k-RMS problem, which is called the Top-k regret minimizing set problem.

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Section: Introductionmentioning

confidence: 99%

“…This was generalized later to the k regret minimizing set [11], where the preference scores of the users top-k choice, is compared with the best in the subset. Following the definition of k-regret minimizing set in [11], we propose faster approximation algorithms for finding small representative sets.…”

Section: Introductionmentioning

confidence: 99%

Faster Approximation Algorithm for the k-Regret Minimizing Set and Related Problems

Kumar

Sintos

2018

2018 Proceedings of the Twentieth Workshop on Algorithm Engineering and Experiments (ALENEX)

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“…The dimensionality of our synthetic dataset varies in the range [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22], with the default being 22-dimensional data. The values in each dimension are generated according to a zipf distribution, for which the skewness parameter is set in the range 0.0 (i.e., uniform) to 0.9 (skewed).…”

Section: Experimental Testbedmentioning

confidence: 99%

“…Generating representative data is one such technique that aims to provide meaningful summary of a potentially large query answer (e.g., [20,31,66,87,97]). In proposed as a practical alternative for both queries [66].…”

Section: Chapter 6 Diversity With Few Regretsmentioning

confidence: 99%

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Scalable diversification for data exploration platforms

Khan¹

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Today, data exploration platforms are widely used to assist users in locating interesting objects within large volumes of scientific and business data. In those platforms, users try to make sense of the underlying data space by iteratively posing numerous queries over large databases.Hence, data exploration platforms rely on methods for the extraction of representative data to provide users with a concise and meaningful representation of query results. That is, extracting a few tuples from a query result to provide quick insights in the potentially huge answer space.In the past few years, importance of diversification while extracting representative subsets of data has been greatly emphasized. It has been shown that diverse subsets provide more effective representation of the underlying data by minimizing redundancy and increasing coverage.Meanwhile, search results diversification adds additional cost to an already computationally expensive exploration process.In this PhD thesis, we have focused on the design, implementation and evaluation of scalable diversification algorithms and schemes for the data exploration platforms. Particularly, this research stipulates that extracting diverse representative results during data exploration requires addressing several challenges including: 1) scaling to big volumes of high dimensional data, 2) large number of users, and 3) enabling real time continuous exploration. To address those challenges we focus on two broad aspects: 1) Diversification of high dimensional large data sets and 2) Diversification of multiple user queries.The existing work conducts diversification in two steps: first compute all relevant query results, and then diversify the query results to select a small diverse subset. Similarly, all the dimensional attributes of all the data points in a query result are considered for diversification. Such a generic approach would be a performance bottleneck in high-dimensional large databases. To efficiently compute diverse subsets of query results exhibiting both high dimensionality and high-cardinality, we have proposed the Progressive Diversification Scheme. Our proposed scheme, utilizes the partial distance computations to reduce the amount of CPU and I/O incurred during query diversification. Moreover, to avoid the overhead of computing all relevant results first, we propose embedding diversification in query evaluation step by utilizing column-based data storage systems. In addition to computational cost of diversification methods, we have also considered the complexity of diversity objective function in high dimensional databases. Often, computing diverse solutions along all the dimensions is not a realistic approach. In fact, users may have some pre-specified preferences over some dimensions of the data, while expecting good coverage over the other dimensions. Motivated by that need, we propose a novel scheme, which aims to generate representative data that balance the tradeoff iii between regret minimization and diversity maximization. Our scheme...

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