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Skip Lists: A Probabilistic Alternative to Balanced Trees
, 1990
"... Skip lists are data structures thla t use probabilistic balancing rather than strictly enforced balancing. As a result, the algorithms for insertion and deletion in skip lists are much simpler and significantly faster than equivalent algorithms for balanced trees. ..."
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Cited by 410 (1 self)
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Skip lists are data structures thla t use probabilistic balancing rather than strictly enforced balancing. As a result, the algorithms for insertion and deletion in skip lists are much simpler and significantly faster than equivalent algorithms for balanced trees.
Data Structures for Traveling Salesmen
, 1995
"... The choice of data structure for tour representation plays a critical role in the efficiency of local improvement heuristics for the Traveling Salesman Problem. The tour data structure must permit queries about the relative order of cities in the current tour and must allow sections of the tour to b ..."
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Cited by 34 (2 self)
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The choice of data structure for tour representation plays a critical role in the efficiency of local improvement heuristics for the Traveling Salesman Problem. The tour data structure must permit queries about the relative order of cities in the current tour and must allow sections of the tour to be reversed. The traditional arraybased representation of a tour permits the relative order of cities to be determined in small constant time, but requires worstcase W(N) time (where N is the number of cities) to implement a reversal, which renders it impractical for large instances. This paper considers alternative tour data structures, examining them from both a theoretical and experimental point of view. The first alternative we consider is a data structure based on splay trees, where all queries and updates take amortized time O(logN). We show that this is close to the best possible, because in the cell probe model of computation any data structure must take worstcase amortized time W(...
Adaptive Structuring Of Binary Search Trees Using Conditional Rotations
 IEEE TRANSACTIONS ON KNOWLEDGE & DATA ENGINEERING
, 1987
"... Consider a set A = {A 1 , A 2 ,...,A N } of records, where each record is identified by a unique key. The records are accessed based on a set of access probabilities S = [s 1 ,s 2 ,...,s N ] and are to be arranged lexicographically using a Binary Search Tree (BST). If S is known a priori, it ..."
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Cited by 8 (3 self)
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Consider a set A = {A 1 , A 2 ,...,A N } of records, where each record is identified by a unique key. The records are accessed based on a set of access probabilities S = [s 1 ,s 2 ,...,s N ] and are to be arranged lexicographically using a Binary Search Tree (BST). If S is known a priori, it is well known [10] that an optimal BST may be constructed using A and S. We consider the case when S is not known a priori . A new restructuring heuristic is introduced that requires three extra integer memory locations per record. In this scheme the restructuring is performed only if it decreases the Weighted Path Length (WPL) of the overall resultant tree. An optimized version of the latter method which requires only one extra integer field per record has also been presented. Initial simulation results which compare our algorithm with various other static and dynamic schemes seem to indicate that this scheme asymptotically produces trees which are an order of magnitude closer to the optim...
An Overview over RedBlack and Finger Trees
, 1992
"... 2 1 1 Figure 1: A redblack tree. The darkened nodes are black nodes. The external nodes are denoted by squares. Shown with each node is its rank. Wyk give another, simpler, implementation of finger trees. They describe a finger data structure which is a modification of redblack trees, but othe ..."
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2 1 1 Figure 1: A redblack tree. The darkened nodes are black nodes. The external nodes are denoted by squares. Shown with each node is its rank. Wyk give another, simpler, implementation of finger trees. They describe a finger data structure which is a modification of redblack trees, but other forms of balanced trees could be used as a basis for the structure. The two problems presented in Chapters 3 and 4 rely on the use of redblack and finger trees respectively. In this chapter we give a fairly complete overview of redblack trees, of the finger trees introduced by Tarjan and Van Wyk, and of a variant of these which we use in Chapter 4. The material here is intended to be comprehensive and useful as an introduction to these two types of data structures. Re  ack rees A redblack tree is a full binary tree in which each node is assigned a color, either red or black. The leaves are called