A new polynomial-time algorithm for linear programming
Combinatorica
On the Average Number of Maxima in a Set of Vectors and Applications
Journal of the ACM (JACM)
The onion technique: indexing for linear optimization queries
SIGMOD '00 Proceedings of the 2000 ACM SIGMOD international conference on Management of data
PREFER: a system for the efficient execution of multi-parametric ranked queries
SIGMOD '01 Proceedings of the 2001 ACM SIGMOD international conference on Management of data
Introduction to Linear Optimization
Introduction to Linear Optimization
Finding k-dominant skylines in high dimensional space
Proceedings of the 2006 ACM SIGMOD international conference on Management of data
Algorithms and analyses for maximal vector computation
The VLDB Journal — The International Journal on Very Large Data Bases
A survey of top-k query processing techniques in relational database systems
ACM Computing Surveys (CSUR)
Continuous Top-k Dominating Queries in Subspaces
PCI '08 Proceedings of the 2008 Panhellenic Conference on Informatics
Personalized top-k skyline queries in high-dimensional space
Information Systems
Top-k dominating queries in uncertain databases
Proceedings of the 12th International Conference on Extending Database Technology: Advances in Database Technology
On Skylining with Flexible Dominance Relation
ICDE '08 Proceedings of the 2008 IEEE 24th International Conference on Data Engineering
Distance-Based Representative Skyline
ICDE '09 Proceedings of the 2009 IEEE International Conference on Data Engineering
Multi-dimensional top-k dominating queries
The VLDB Journal — The International Journal on Very Large Data Bases
Discovering relative importance of skyline attributes
Proceedings of the VLDB Endowment
Threshold-based probabilistic top-k dominating queries
The VLDB Journal — The International Journal on Very Large Data Bases
Top-k skyline: a unified approach
OTM'05 Proceedings of the 2005 OTM Confederated international conference on On the Move to Meaningful Internet Systems
EDBT'06 Proceedings of the 10th international conference on Advances in Database Technology
Domination mining and querying
DaWaK'07 Proceedings of the 9th international conference on Data Warehousing and Knowledge Discovery
(Approximate) uncertain skylines
Proceedings of the 14th International Conference on Database Theory
Interactive regret minimization
SIGMOD '12 Proceedings of the 2012 ACM SIGMOD International Conference on Management of Data
From stars to galaxies: skyline queries on aggregate data
Proceedings of the 16th International Conference on Extending Database Technology
Top-k diversity queries over bounded regions
ACM Transactions on Database Systems (TODS)
SkyView: a user evaluation of the skyline operator
Proceedings of the 22nd ACM international conference on Conference on information & knowledge management
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We propose the k-representative regret minimization query (k-regret) as an operation to support multi-criteria decision making. Like top-k, the k-regret query assumes that users have some utility or scoring functions; however, it never asks the users to provide such functions. Like skyline, it filters out a set of interesting points from a potentially large database based on the users' criteria; however, it never overwhelms the users by outputting too many tuples. In particular, for any number k and any class of utility functions, the k-regret query outputs k tuples from the database and tries to minimize the maximum regret ratio. This captures how disappointed a user could be had she seen k representative tuples instead of the whole database. We focus on the class of linear utility functions, which is widely applicable. The first challenge of this approach is that it is not clear if the maximum regret ratio would be small, or even bounded. We answer this question affirmatively. Theoretically, we prove that the maximum regret ratio can be bounded and this bound is independent of the database size. Moreover, our extensive experiments on real and synthetic datasets suggest that in practice the maximum regret ratio is reasonably small. Additionally, algorithms developed in this paper are practical as they run in linear time in the size of the database and the experiments show that their running time is small when they run on top of the skyline operation which means that these algorithm could be integrated into current database systems.