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Binary Search Trees of Almost Optimal Height
 ACTA INFORMATICA
, 1990
"... First we present a generalization of symmetric binary Btrees, SBB(k) trees. The obtained structure has a height of only \Sigma (1 + 1k) log(n + 1)\Upsilon, where k may be chosen to be any positive integer. The maintenance algorithms require only a constant number of rotations per updating operati ..."
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First we present a generalization of symmetric binary Btrees, SBB(k) trees. The obtained structure has a height of only \Sigma (1 + 1k) log(n + 1)\Upsilon, where k may be chosen to be any positive integer. The maintenance algorithms require only a constant number of rotations per updating operation in the worst case. These properties together with the fact that the structure is relatively simple to implement makes it a useful alternative to other search trees in practical applications. Then, by using an SBB(k)tree with a varying k we achieve a structure with a logarithmic amortized cost per update and a height of log n + o(log n). This result is an improvement of the upper bound on the height of a dynamic binary search tree. By maintaining two trees simultaneously the amortized cost is transformed into a worstcase cost. Thus, we have improved the worstcase complexity of the dictionary problem.
Comparisonefficient and Writeoptimal Searching and Sorting
 In ISA'91, volume 557 of LNCS
, 1991
"... We consider the problem of updating a binary search tree in O(log n) amortized time while using as few comparisons as possible. We show that a tree of height dlog(n+1)+1= p log(n + 1)e can be maintained in O(log n) amortized time such that the difference between the longest and shortest paths fr ..."
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Cited by 4 (1 self)
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We consider the problem of updating a binary search tree in O(log n) amortized time while using as few comparisons as possible. We show that a tree of height dlog(n+1)+1= p log(n + 1)e can be maintained in O(log n) amortized time such that the difference between the longest and shortest paths from the root to an external node is at most 2. We also study the problem of sorting and searching in the slow write model of computation, where we have a constant size cache of fast memory and a large amount of memory with a much slower writing time than reading time. In such a model, it is important to sort using only \Theta(n) writes into the slower memory. We say that such algorithms are write optimal, and we introduce a O(n log n) time, writeoptimal sorting algorithm that requires only n log n+O(n) comparisons in the worst case. No previous sorting algorithm that performs n log n + o(n log n) comparisons in the worst case had previously been shown to be write optimal. The above results ...
Optimal Bounds on the Dictionary Problem
 In Proc. Symp. on Optimal Algorithms, Varna, volume 401 of LNCS
, 1989
"... A new data structure for the dictionary problem is presented. Updates are performed in \Theta(log n) time in the worst case and the number of comparisons per operation is dlog n + 1 + ffle, where ffl is an arbitrary positive constant. 1 Introduction One of the fundamental and most studied problems ..."
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Cited by 4 (1 self)
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A new data structure for the dictionary problem is presented. Updates are performed in \Theta(log n) time in the worst case and the number of comparisons per operation is dlog n + 1 + ffle, where ffl is an arbitrary positive constant. 1 Introduction One of the fundamental and most studied problems in computer science is the dictionary problem, that is the problem of how to maintain a set of data during the operations search, insert and delete. It is well known that in a comparisonbased model the lower bound on these operations is dlog(n + 1)e comparisons both in the average and in the worst case. This bound can be achieved by storing the set in an array or in a perfectly balanced binary search tree. However, for both these data structures the overhead cost per update is high, \Theta(n) in the worst case. An efficient dynamic data structure for the dictionary problem should have a worst case cost of \Theta(log n) per operation. The first efficient solution was presented by AdelsonVel...