AVL-trees for localized search
Information and Control
Splitsort—an adaptive sorting algorithm
Information Processing Letters
A survey of adaptive sorting algorithms
ACM Computing Surveys (CSUR)
A framework for adaptive sorting
Discrete Applied Mathematics
Splaysort: fast, versatile, practical
Software—Practice & Experience
On the Dynamic Finger Conjecture for Splay Trees. Part II: The Proof
SIAM Journal on Computing
Space-efficient finger search on degree-balanced search trees
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Amortized Complexity of Bulk Updates in AVL-Trees
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Proceedings of the 4th GI-Conference on Theoretical Computer Science
Local Insertion Sort Revisited
Proceedings of the International Symposium on Optimal Algorithms
Adaptive sorting: an information theoretic perspective
Acta Informatica
An empirical study for inversions-sensitive sorting algorithms
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
Two constant-factor-optimal realizations of adaptive heapsort
IWOCA'11 Proceedings of the 22nd international conference on Combinatorial Algorithms
The weak-heap data structure: Variants and applications
Journal of Discrete Algorithms
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Well-known measures of presortedness, among others, are the number of inversions needed to sort the input sequence, or the minimal number of blocks of consecutive elements that remain as such in the sorted sequence. In this paper we study the problem of possible composition of measures. For example, after determining the blocks in an input sequence, it is meaningful to measure how many inversions of the blocks are needed to finally sort the sequence. With composite measures in mind we introduce the idea of applying bulk insertions to improve adaptive binary-tree (AVL) sorting; this is done by combining local insertion sort with bulk-insertion methods. We show that bulk-insertion sort is optimally adaptive with respect to the number of bulks and with respect to the number of inversions in the original input. As to composite measures, we define a new measure that tells how many inversions are needed when the extracted bulks form the input. Bulk-insertion sort is shown to be adaptive with respect to this measure. Our experiments show that applying bulk insertion in AVL-tree sorting considerably reduces the number of comparisons and time needed to sort nearly sorted sequences.