Fuzzy queries in multimedia database systems
PODS '98 Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
On the hardness of approximating minimization problems
Journal of the ACM (JACM)
Combining fuzzy information from multiple systems
Journal of Computer and System Sciences
On the Average Number of Maxima in a Set of Vectors and Applications
Journal of the ACM (JACM)
A formula for incorporating weights into scoring rules
Theoretical Computer Science - Special issue on the 6th International Conference on Database Theory—ICDT '97
Multiobjective query optimization
PODS '01 Proceedings of the twentieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Optimal aggregation algorithms for middleware
PODS '01 Proceedings of the twentieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Approximation algorithms
Efficient Progressive Skyline Computation
Proceedings of the 27th International Conference on Very Large Data Bases
On the approximability of trade-offs and optimal access of Web sources
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Improved approximation algorithms for geometric set cover
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Efficient skyline computation over low-cardinality domains
VLDB '07 Proceedings of the 33rd international conference on Very large data bases
Succinct approximate convex pareto curves
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Small Approximate Pareto Sets for Bi-objective Shortest Paths and Other Problems
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
(Approximate) uncertain skylines
Proceedings of the 14th International Conference on Database Theory
Small Approximate Pareto Sets for Biobjective Shortest Paths and Other Problems
SIAM Journal on Computing
Prioritized repairing and consistent query answering in relational databases
Annals of Mathematics and Artificial Intelligence
Domination mining and querying
DaWaK'07 Proceedings of the 9th international conference on Data Warehousing and Knowledge Discovery
Skyline probability over uncertain preferences
Proceedings of the 16th International Conference on Extending Database Technology
Skyline queries, front and back
ACM SIGMOD Record
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We propose and investigate from the algorithmic standpoint a novel form of fuzzy query called approximately dominating representatives or ADRs. The ADRs of a multidimensional point set consist of a few points guaranteed to contain an approximate optimum of any monotone Lipschitz continuous combining function of the dimensions. ADRs can be computed by appropriately post-processing Pareto, or ''skyline'', queries [Kian-Lee Tan, Pin-Kwang Eng, Beng Chin Ooi, Efficient progressive skyline computation, in: VLDB, 2001, pp. 301-310; Wolf-Tilo Balke, Ulrich Guntzer, Jason Xin Zheng, Efficient distributed skylining for web information systems, in: EDBT, 2004. [14]]. We show that the problem of minimizing the number of points returned, for a user-specified desired approximation, can be solved in polynomial time in two dimensions; for three and more it is NP-hard but has a polynomial-time logarithmic approximation. Finally, we present a polynomial-time, constant factor approximation algorithm for three dimensions.