The input/output complexity of sorting and related problems
Communications of the ACM
Deterministic distribution sort in shared and distributed memory multiprocessors
SPAA '93 Proceedings of the fifth annual ACM symposium on Parallel algorithms and architectures
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Expected time bounds for selection
Communications of the ACM
Approximate and Exact Deterministic Parallel Selection
MFCS '93 Proceedings of the 18th International Symposium on Mathematical Foundations of Computer Science
Linear-time In-place Selection in Less than 3n Comparisons
ISAAC '95 Proceedings of the 6th International Symposium on Algorithms and Computation
Euro-Par '97 Proceedings of the Third International Euro-Par Conference on Parallel Processing
Proceedings of the Tenth Conference on Foundations of Software Technology and Theoretical Computer Science
Algorithms and data structures for external memory
Foundations and Trends® in Theoretical Computer Science
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Sequential selection has been solved in linear time by Blum et al. [M.B. Blum, R.W. Floyd, V.R. Pratt, R.L. Rivest, R.E. Tarjan, Time bounds for selection, J. Comput. System Sci. 7 (4) (1972) 448-461 ]. Running this algorithm on a problem of size N with N M, the size of the main-memory, results in an algorithm that reads and writes O(N) elements, while the number of comparisons is also bounded by O(N). This is asymptotically optimal, but the constants are so large that in practice sorting is faster for most values of M and N.This paper provides the first detailed study of the external selection problem. A randomized algorithm of a conventional type is close to optimal in all respects. Our deterministic algorithm is more or less the same, but first the algorithm builds an index structure of all the elements. This effort is not wasted: the index structure allows the retrieval of elements so that we do not need a second scan through all the data. This index structure can also be used for repeated selections, and can be extended over time. For a problem of size N, the deterministic algorithm reads N + o(N) elements and writes only o(N) elements and is thereby optimal to within lower-order terms.