Amortized efficiency of list update and paging rules
Communications of the ACM
Self-adjusting binary search trees
Journal of the ACM (JACM)
Sequential access in splay trees takes linear time
Combinatorica
The input/output complexity of sorting and related problems
Communications of the ACM
Lower bounds for accessing binary search trees with rotations
SIAM Journal on Computing
Skip lists: a probabilistic alternative to balanced trees
Communications of the ACM
Self-adjusting multi-way search trees
Information Processing Letters
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
A lower bound for randomized list update algorithms
Information Processing Letters
Improved Randomized On-Line Algorithms for the List Update Problem
SIAM Journal on Computing
Alternatives to splay trees with O(log n) worst-case access times
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Biased dictionaries with fast insert/deletes
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
On the Dynamic Finger Conjecture for Splay Trees. Part I: Splay Sorting log n-Block Sequences
SIAM Journal on Computing
On the Dynamic Finger Conjecture for Splay Trees. Part II: The Proof
SIAM Journal on Computing
Algorithm Design and Software Libraries: Recent Developments in the LEDA Project
Proceedings of the IFIP 12th World Computer Congress on Algorithms, Software, Architecture - Information Processing '92, Volume 1 - Volume I
Self-Adjusting k-ary Search Trees
WADS '89 Proceedings of the Workshop on Algorithms and Data Structures
Self-adjusting Data Structures for External Memory String Access
Self-adjusting Data Structures for External Memory String Access
On the sequential access theorem and deque conjecture for splay trees
Theoretical Computer Science
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
O(log log n)-competitive dynamic binary search trees
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A data structure for a sequence of string accesses in external memory
ACM Transactions on Algorithms (TALG)
Exploring the duality between skip lists and binary search trees
ACM-SE 45 Proceedings of the 45th annual southeast regional conference
A unified access bound on comparison-based dynamic dictionaries
Theoretical Computer Science
How to splay for loglogn-competitiveness
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
A Distribution-Sensitive Dictionary with Low Space Overhead
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Simplified self-adapting skip lists
IDEAL'10 Proceedings of the 11th international conference on Intelligent data engineering and automated learning
Skip lift: a probabilistic alternative to red-black trees
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
A static optimality transformation with applications to planar point location
Proceedings of the twenty-seventh annual symposium on Computational geometry
A distribution-sensitive dictionary with low space overhead
Journal of Discrete Algorithms
Parameterized analysis of paging and list update algorithms
WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
Skip lift: A probabilistic alternative to red-black trees
Journal of Discrete Algorithms
A new perspective on list update: probabilistic locality and working set
WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
De-amortizing binary search trees
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
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Sleator and Tarjan [39] conjectured that splay trees are dynamically optimal binary search trees (BST). In this context, we study the skip list data structure introduced by Pugh [35]. We prove that for a class of skip lists that satisfy a weak balancing property, the working-set bound is a lower bound on the time to access any sequence. Furthermore, we develop a deterministic self-adjusting skip list whose running time matches the working-set bound, thereby achieving dynamic optimality in this class. Finally, we highlight the implications our bounds for skip lists have on multi-way branching search trees such as B-trees, (a-b)-trees, and other variants as well as their binary tree representations. In particular, we show a self-adjusting B-tree that is dynamically optimal both in internal and external memory.