An in-place sorting with O(nlog n) comparisons and O(n) moves

We present the first in-place algorithm for sorting an array of size n that performs, in the worst case, at most O(nlog n) element comparisons and O(n) element transports.This solves a long-standing open problem, stated explicitly, for example, in Munro and Raman [1992], of whether there exists a sorting algorithm that matches the asymptotic lower bounds on all computational resources simultaneously.

[1]  Venkatesh Raman.  Sorting in-place with minimum data movement , 1992 .

[2]  Paul M. B. Vitányi,et al.  An Introduction to Kolmogorov Complexity and Its Applications , 1993, Graduate Texts in Computer Science.

[3]  Donald E. Knuth,et al.  The art of computer programming: sorting and searching (volume 3) , 1973 .

[4]  Gianni Franceschini.  An in-place sorting algorithm performing $O(n\log n)$ comparisons and $O(n)$ data moves , 2003 .

[5]  Jyrki Katajainen,et al.  In-Place Sorting with Fewer Moves , 1999, Inf. Process. Lett..

[6]  Venkatesh Raman,et al.  Fast stable in-place sorting withO(n) data moves , 1996, Algorithmica.

[7]  Dan Suciu,et al.  Journal of the ACM , 2006 .

[8]  Alon Itai,et al.  A Sparse Table Implementation of Priority Queues , 1981, ICALP.

[9]  Jyrki Katajainen,et al.  Asymptotically efficient in-place merging , 2000, Theor. Comput. Sci..

[10]  Donald E. Knuth,et al.  The art of computer programming, volume 3: (2nd ed.) sorting and searching , 1998 .

[11]  William I. Gasarch,et al.  Book Review: An introduction to Kolmogorov Complexity and its Applications Second Edition, 1997 by Ming Li and Paul Vitanyi (Springer (Graduate Text Series)) , 1997, SIGACT News.

[12]  Jukka Teuhola,et al.  Practical In-Place Mergesort , 1996, Nord. J. Comput..

[13]  Venkatesh Raman,et al.  Sorting with Minimum Data Movement , 1992, J. Algorithms.

[14]  Robert Sedgewick,et al.  The Analysis of Heapsort , 1993, J. Algorithms.

[15]  K. Reinhardt.  Sorting In-Place with a Worst Case Complexity of n log n − 1 . 3 n + O ( log n ) Comparisons and ε n log n + O ( 1 ) Transports ∗ , 1992 .

[16]  Dan E. Willard,et al.  Maintaining dense sequential files in a dynamic environment (Extended Abstract) , 1982, STOC '82.

[17]  Klaus Reinhardt.  Sorting In-Place with a Worst Case Complexity of n log n-1.3n + O(logn) Comparisons and epsilon n log n + O(1) Transports , 1992, ISAAC.

[18]  Venkatesh Raman,et al.  Selection from Read-Only Memory and Sorting with Minimum Data Movement , 1996, Theor. Comput. Sci..

[19]  Ming Li,et al.  An Introduction to Kolmogorov Complexity and Its Applications , 2019, Texts in Computer Science.

[20]  Ingo Wegener.  BOTTOM-UP-HEAPSORT, a New Variant of HEAPSORT, Beating, on an Average, QUICKSORT (if n is not Very Small) , 1993, Theor. Comput. Sci..