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A unified access bound on comparisonbased dynamic dictionaries
 Theoretical Computer Science
"... We present a dynamic comparisonbased search structure that supports insertions, deletions, and searches within the unified bound. The unified bound specifies that it is quick to access an element that is near a recently accessed element. More precisely, if w(y) distinct elements have been accessed ..."
Abstract

Cited by 12 (1 self)
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We present a dynamic comparisonbased search structure that supports insertions, deletions, and searches within the unified bound. The unified bound specifies that it is quick to access an element that is near a recently accessed element. More precisely, if w(y) distinct elements have been accessed since the last access to element y, and d(x, y) denotes the rank distance between x and y among the current set of elements, then the amortized cost to access element x is O(miny log[w(y) + d(x, y) + 2]). This property generalizes the workingset and dynamicfinger properties of splay trees. Preprint submitted to Elsevier Science 31 January 2007 1
Key independent optimality
 In International Symp. on Algorithms and Computation
, 2002
"... A new form of optimality for comparison based static dictionaries is introduced. This type of optimality, keyindependent optimality, is motivated by applications that assign key values randomly. It is shown that any data structure that is keyindependently optimal is expected to execute any access s ..."
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Cited by 8 (2 self)
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A new form of optimality for comparison based static dictionaries is introduced. This type of optimality, keyindependent optimality, is motivated by applications that assign key values randomly. It is shown that any data structure that is keyindependently 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 keyindependent optimality. Splay trees are shown to be keyindependently optimal. 1
Advanced Data Structures JanApr 2012 Lecturer: Venkatesh Raman
, 2012
"... In the last lecture we studied MovetoFront (MTF) Heuristic for a list and its competitive ratio. We also introduced Binary Search Trees (BST) and optimal BSTs. In today’s lecture, we will be analysing Splay Trees and see that they perform as well as an optimal static BST without maintaining extra ..."
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In the last lecture we studied MovetoFront (MTF) Heuristic for a list and its competitive ratio. We also introduced Binary Search Trees (BST) and optimal BSTs. In today’s lecture, we will be analysing Splay Trees and see that they perform as well as an optimal static BST without maintaining extra information for balancing the tree. We also discuss the scenario when we have the freedom to begin the search anywhere instead of always starting from the root node. 2 Statically Optimal Search Given a sequence of length m and having n distinct elements. We look at the elements one by one. We want to implement following operations: • insert (i) – If i has not been seen so far in the sequence, insert it in the tree. • access(i) – If i exists in the tree, return a pointer to it. Operation of insert(i) is O(n 2) atmost. We can ignore insertion and w.l.o.g assume we have a tree with all the keys initially and we are performing a sequence of access(i) operations on it. 2.1 Information Entropy and Search Given a set of keys S = [1... n], and frequency of access pi for i ∈ S. The information entropy H is, H = − ∑ piln(pi)