Dynamic optimality for skip lists and B-trees

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Dynamic optimality for skip lists and B-trees
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, (ab)-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.
Prosenjit Bose, Karim Douïeb, Stefan Langerma
Added 30 Oct 2010
Updated 30 Oct 2010
Type Conference
Year 2008
Where SODA
Authors Prosenjit Bose, Karim Douïeb, Stefan Langerman
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