The input/output complexity of sorting and related problems
Communications of the ACM
Computing dominances inEn (short communication)
Information Processing Letters
On Finding the Maxima of a Set of Vectors
Journal of the ACM (JACM)
On the Average Number of Maxima in a Set of Vectors and Applications
Journal of the ACM (JACM)
Output-size sensitive algorithms for finding maximal vectors
SCG '85 Proceedings of the first annual symposium on Computational geometry
Dynamic Maintenance of Maxima of 2-d Point Sets
SIAM Journal on Computing
Multidimensional divide-and-conquer
Communications of the ACM
Proceedings of the 17th International Conference on Data Engineering
A General Lower Bound on the I/O-Complexity of Comparison-based Algorithms
WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
Scaling and related techniques for geometry problems
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Stabbing the Sky: Efficient Skyline Computation over Sliding Windows
ICDE '05 Proceedings of the 21st International Conference on Data Engineering
Progressive skyline computation in database systems
ACM Transactions on Database Systems (TODS) - Special Issue: SIGMOD/PODS 2003
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
Shooting stars in the sky: an online algorithm for skyline queries
VLDB '02 Proceedings of the 28th international conference on Very Large Data Bases
Efficient skyline computation over low-cardinality domains
VLDB '07 Proceedings of the 33rd international conference on Very large data bases
Algorithms and data structures for external memory
Foundations and Trends® in Theoretical Computer Science
External-memory computational geometry
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Efficient sort-based skyline evaluation
ACM Transactions on Database Systems (TODS)
On Skylining with Flexible Dominance Relation
ICDE '08 Proceedings of the 2008 IEEE 24th International Conference on Data Engineering
Randomized multi-pass streaming skyline algorithms
Proceedings of the VLDB Endowment
Journal of Computer and System Sciences
Instance-Optimal Geometric Algorithms
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
On finding skylines in external memory
Proceedings of the thirtieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Orthogonal range searching on the RAM, revisited
Proceedings of the twenty-seventh annual symposium on Computational geometry
Dynamic planar range maxima queries
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
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We consider the skyline problem (aka the maxima problem), which has been extensively studied in the database community. The input is a set P of d-dimensional points. A point dominates another if the coordinate of the former is at most that of the latter on every dimension. The goal is to find the skyline, which is the set of points p ∈ P such that p is not dominated by any other point in P. The main result of this article is that, for any fixed dimensionality d ≥ 3, in external memory the skyline problem can be settled by performing O((N/B)logM/Bd−2(N/B)) I/Os in the worst case, where N is the cardinality of P, B the size of a disk block, and M the capacity of main memory. Similar bounds can also be achieved for computing several skyline variants, including the k-dominant skyline, k-skyband, and α-skyline. Furthermore, the performance can be improved if some dimensions of the data space have small domains. When the dimensionality d is not fixed, the challenge is to outperform the naive algorithm that simply checks all pairs of points in P × P. We give an algorithm that terminates in O((N/B) logd − 2 N) I/Os, thus beating the naive solution for any d = O(log N / log log N).