Skip lift: A probabilistic alternative to red-black trees

We present the Skip lift, a randomized dictionary data structure inspired by the skip list [Pugh90, Comm. of the ACM]. Similar to the skip list, the skip lift has the finger search property: given a pointer to an arbitrary element f, searching for an element x takes expected O(logδ) time where δ is the rank distance between the elements x and f. The skip lift uses nodes of O(1) worst-case size (for a total of O(n) worst-case space usage) and it is one of the few efficient dictionary data structures that performs an O(1) worst-case number of structural changes (pointers/fields modifications) during an update operation. Given a pointer to the element to be removed from the skip lift the deletion operation takes O(1) worst-case time

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

Layered working-set trees

The working-set bound [Sleator and Tarjan in J. ACM 32(3), 652-686, 1985] roughly states that searching for an element is fast if the element was accessed recently. Binary search trees, such as splay trees, can achieve this property in the amortized sense, while data structures that are not binary search trees are known to have this property in the worst case. We close this gap and present a binary search tree called a layered working-set tree that guarantees the working-set property in the worst case. The unified bound [B?adoiu et al. in Theor. Comput. Sci. 382(2), 86-96, 2007] roughly states that searching for an element is fast if it is near (in terms of rank distance) to a recently accessed element.We show how layered working-set trees can be used to achieve the unified bound to within a small additive term in the amortized sense while maintaining in the worst case an access time that is both logarithmic and within a small multiplicative factor of the working-set bound

Assessing the Pacific benefits of trade and economic interdependence in the Middle East and North Africa

The working-set bound [Sleator and Tarjan, J. ACM, 1985] roughly states that searching for an element is fast if the element was accessed recently. Binary search trees, such as splay trees, can achieve this property in the amortized sense, while data structures that are not binary search trees are known to have this property in the worst case. We close this gap and present a binary search tree called a layered working-set tree that guarantees the working-set property in the worst case. The unified bound [B

Fast local searches and updates in bounded universes

Given a bounded universe {0,1,⋯,U-1}, we show how to perform predecessor searches in O(loglogΔ) expected time, where Δ is the difference between the element being searched for and its predecessor in the structure, while supporting updates in O(loglogΔ) expected amortized time, as well. This unifies the results of traditional bounded universe structures (which support predecessor searches in O(loglogU) time) and hashing (which supports membership queries in O(1) time). We also show how these results can be applied to approximate nearest neighbour queries and range searching

Dynamic hotlinks

SCOPUS: cp.jinfo:eu-repo/semantics/publishe