Improved upper bounds on Shellsort
Journal of Computer and System Sciences
Shellsort with three increments
Random Structures & Algorithms - Special issue: average-case analysis of algorithms
An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Sorting Using Networks of Queues and Stacks
Journal of the ACM (JACM)
A high-speed sorting procedure
Communications of the ACM
New Applications of the Incompressibility Method
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Analysis of Shellsort and Related Algorithms
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
Shellsort and sorting networks
Shellsort and sorting networks
Improved lower bounds for Shellsort
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
New Applications of the Incompressibility Method
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
On the Performance of WEAK-HEAPSORT
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
SOFSEM '00 Proceedings of the 27th Conference on Current Trends in Theory and Practice of Informatics
Asymptotic Complexity from Experiments? A Case Study for Randomized Algorithms
WAE '00 Proceedings of the 4th International Workshop on Algorithm Engineering
Best Increments for the Average Case of Shellsort
FCT '01 Proceedings of the 13th International Symposium on Fundamentals of Computation Theory
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We prove a general lower bound on the average-case complexity of Shellsort: the average number of data-movements (and comparisons) made by a p-pass Shellsort for any incremental sequence is Ω(pn1+1=p) for every p. The proof method is an incompressibility argument based on Kolmogorov complexity. Using similar techniques, the average-case complexity of several other sorting algorithms is analyzed.