Showing papers on "Splay tree published in 2005"
01 Jan 2005
TL;DR: In this article, it was shown that pairing heaps can support all priority queue operations in logarithmic time and is known to be extremely efficient in practice, even for splay trees.
Abstract: Fredman, Sedgewick, Sleator, and Tarjan proposed the
{em pairing heap}
as a self-adjusting, streamlined version of the Fibonacci heap.
It provably supports all priority queue operations in logarithmic
time and is known to be extremely efficient in practice.
However, despite its simplicity and empirical superiority,
the pairing heap is one of the few popular data structures
whose basic complexity remains open.
In this paper we prove that pairing heaps support the
deletemin operation in optimal logarithmic time and all other operations
(insert, meld, and decreasekey) in time
$O(2^{2sqrt{loglog n}})$. This result gives
the {em first} sub-logarithmic time bound for decreasekey
and comes close to the
lower bound of $Omega(loglog n)$ established by Fredman.
Pairing heaps have a well known but poorly understood relationship to
splay trees and, to date, the transfer of ideas has flowed in one direction:
from splaying to pairing. One contribution of this paper is a
new analysis that reasons explicitly with information-theoretic
measures. Whether these ideas could contribute to the analysis
of splay trees is an open question.
45 citations
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.
39 citations
TL;DR: It is proved that chain-splay is loglogN-competitive to any off-line searching algorithm, which is the nearest point to dynamic optimality of splay trees reached since 1983.
Abstract: We present an extension of the splay technique, the chain-splay. Chain-splay trees splay the accessed element to the root exactly as classic splay trees do, but also perform some local ‘house-keeping' splay operations below the accessed element. We prove that chain-splay is loglogN-competitive to any off-line searching algorithm. This result is the nearest point to dynamic optimality of splay trees reached since 1983.
10 citations
01 Mar 2005
Abstract: In this chapter, we present a set of advanced data structures and algorithms for performing searching. The data structures we cover include the red–black tree, the splay tree, and the skip list. AVL trees and red–black trees are two solutions to the problem of handling unbalanced binary search trees. The skip list is an alternative to using a treelike data structure that foregoes the complexity of the red–black and splay trees. AVL Trees Named for the two computer scientists who discovered this data structure—G. M. Adelson-Velskii and E. M. Landis—in 1962, AVL trees provide another solution to maintaining balanced binary trees. The defining characteristic of an AVL tree is that the difference between the height of the right and left subtrees can never be more than one. AVL Tree Fundamentals To guarantee that the tree always stays “in balance,” the AVL tree continually compares the heights of the left and right subtrees. AVL trees utilize a technique, called a rotation, to keep them in balance. To understand how a rotation works, let's look at a simple example that builds a binary tree of integers. Starting with the tree shown in Figure 15.1, if we insert the value 10 into the tree, the tree becomes unbalanced, as shown in Figure 15.2. The left subtree now has a height of 2, but the right subtree has a height of 0, violating the rule for AVL trees.
1 citations
01 Jan 2005
TL;DR: The Interleave Bound for dynamic optimal binary search is discussed, along with some new properties and results, and it is attempted to apply these results to Splay Trees, in the hope of working towards a proof that splay trees are O(lg lg n)-competitive.
Abstract: We give a discussion of the Interleave Bound for dynamic optimal binary search, along with some new properties and results. We attempt to apply these results to Splay Trees, in the hope of working towards a proof that splay trees are O(lg lg n)-competitive. Some partial results and conjectures are formulated.
02 Aug 2005
TL;DR: A splay tree based data structure and an optimal index generation algorithm specifically designed for AS_PATH are proposed, exploiting the innate characteristics of AS_ PATH.
Abstract: With the fast growing size and complexity of core network, the hash based data structure of current AS_PATH implementation in BGP is facing challenges in performance, mainly caused by the static attribute of the simple hash. This paper proposed a splay tree based data structure and an optimal index generation algorithm specifically designed for AS_PATH. Exploiting the innate characteristics of AS_PATH, the proposed algorithm shows superior performance.