Showing papers on "Splay tree published in 2002"
06 Jan 2002
TL;DR: This paper shows that for the case of lists, one can achieve a 1 + e ratio with respect to the best static list in hindsight, by a simple efficient algorithm, and shows a (computationally inefficient) algorithm that achieves "dynamic search optimality": dynamic optimality if the online algorithm to make free rotations after each request.
Abstract: Adaptive data structures form a central topic of on-line algorithms research, beginning with the results of Sleator and Tarjan showing that splay trees achieve static optimality for search trees, and that Move-to-Front is constant competitive for the list update problem [ST85a, ST85b]. This paper is inspired by the observation that one can in fact achieve a 1 + e ratio against the best static object in hindsight for a wide range of data structure problems via "weighted experts" techniques from Machine Learning, if computational decision-making costs are not considered.In this paper, we give two results. First, we show that for the case of lists, we can achieve a 1 + e ratio with respect to the best static list in hindsight, by a simple efficient algorithm. This algorithm can then be combined with existing results to simultaneously achieve good static and dynamic bounds. Second, for trees, we show a (computationally inefficient) algorithm that achieves what we call "dynamic search optimality": dynamic optimality if we allow the online algorithm to make free rotations after each request. We hope this to be a step towards solving the longstanding open problem of achieving true dynamic optimality for trees.
33 citations
TL;DR: It is proved that the randomized splaying scheme has the same asymptotic performance as the original deterministic scheme but improves constants in the expected running time.
33 citations
21 Nov 2002
TL;DR: It is shown that any data structure that is key-independently optimal is expected to execute any access sequence where the key values are assigned arbitrarily to unordered data as fast as any offline binary search tree algorithm, within a multiplicative constant.
Abstract: A new form of optimality for comparison based static dictionaries is introduced. This type of optimality, key-independent optimality, is motivated by applications that assign key values randomly. It is shown that any data structure that is key-independently optimal is expected to execute any access sequence where the key values are assigned arbitrarily to unordered data as fast as any offline binary search tree algorithm, within a multiplicative constant. Asymptotically tight upper and lower bounds are presented for key-independent optimality. Splay trees are shown to be key-independently optimal.
10 citations
03 Jul 2002
TL;DR: It is proved that in general, the bulk operation composed of several simple ones of sizes m1, ..., mk has amortized complexity O(?i=1k log mi) for the tree adjustment phase.
Abstract: A bulk insertion for a given set of keys inserts all keys in the set into a leaf-oriented AVL-tree. Similarly, a bulk deletion deletes them all. The bulk insertion is simple if all keys fall in the same leaf position in the AVL-tree. We prove that simple bulk insertions and deletions of m keys have amortized complexity O(log m) for the tree adjustment phase. Our reasoning implies easy proofs for the amortized constant rebalancing cost of single insertions and deletions in AVL-trees. We prove that in general, the bulk operation composed of several simple ones of sizes m1, ..., mk has amortized complexity O(?i=1k log mi).
4 citations