An implicit data structure supporting insertion, deletion, and search in O(log:OS2:OEn) time
Journal of Computer and System Sciences
Simplified stable merging tasks
Journal of Algorithms
No. 318 on SWAT 88: 1st Scandinavian workshop on algorithm theory
Sorting with minimum data movement
Journal of Algorithms
Selection from read-only memory and sorting with minimum data movement
Theoretical Computer Science
In-place sorting with fewer moves
Information Processing Letters
Sorting Multisets Stably in Minimum Space
SWAT '92 Proceedings of the Third Scandinavian Workshop on Algorithm Theory
An In-Place Sorting with O(n log n) Comparisons and O(n) Moves
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Optimal cache-oblivious implicit dictionaries
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Optimal in-place sorting of vectors and records
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
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We settle a long-standing open question, namely whether it is possible to sort a sequence of n elements stably (i.e. preserving the original relative order of the equal elements), using O(1) auxiliary space and performing O(n log n) comparisons and O(n) data moves. Munro and Raman stated this problem in [J. Algorithms, 13, 1992] and gave an in-place but unstable sorting algorithm that performs O(n) data moves and O(n1+ε) comparisons. Subsequently [Algorithmica, 16, 1996] they presented a stable algorithm with these same bounds. Recently, Franceschini and Geffert [FOCS 2003] presented an unstable sorting algorithm that matches the asymptotic lower bounds on all computational resources.