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Making Data Structures Persistent
, 1989
"... This paper is a study of persistence in data structures. Ordinary data structures are ephemeral in the sense that a change to the structure destroys the old version, leaving only the new version available for use. In contrast, a persistent structure allows access to any version, old or new, at any t ..."
Abstract

Cited by 250 (6 self)
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This paper is a study of persistence in data structures. Ordinary data structures are ephemeral in the sense that a change to the structure destroys the old version, leaving only the new version available for use. In contrast, a persistent structure allows access to any version, old or new, at any time. We develop simple, systematic, and effiient techniques for making linked data structures persistent. We use our techniques to devise persistent forms of binary search trees with logarithmic access, insertion, and deletion times and O(1) space bounds for insertion and deletion.
Range mode and range median queries on lists and trees
 In Proceedings of the 14th Annual International Symposium on Algorithms and Computation (ISAAC
, 2003
"... ABSTRACT. We consider algorithms for preprocessing labelled lists and trees so that, for any two nodes u and v we can answer queries of the form: What is the mode or median label in the sequence of labels on the path from u to v. 1 ..."
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Cited by 16 (3 self)
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ABSTRACT. We consider algorithms for preprocessing labelled lists and trees so that, for any two nodes u and v we can answer queries of the form: What is the mode or median label in the sequence of labels on the path from u to v. 1
Thesis Summary The Diameter of Permutation Groups Fully Persistent Search Trees
, 1986
"... This thesis comprise two disjoint topics: the diameter of permutation groups and fully persistent search trees. The diameter of a permutation group is the length of the longest product of generators required to reach a group element. For example, the diameter of a permutation group puzzle like Rubik ..."
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This thesis comprise two disjoint topics: the diameter of permutation groups and fully persistent search trees. The diameter of a permutation group is the length of the longest product of generators required to reach a group element. For example, the diameter of a permutation group puzzle like Rubik's Cube is the.,largest number of moves necessary to solve the puzzle. There are well known polynomialtime algorithims to determine if it is possible to reach a particular permutation with a given set of generators, but these algorithms can give a product exponentially longer than is required. We show that if the generators are constrained to be cycles with degree bounded by a constant then the diameter of the group is O(n2). Moreover, an O(n 2) length product expressing a given permutation can be found in polynomial time. A persistent search tree differs from an ordinary search tree in that after an insertion or deletion, the old version of the tree can still be searched. This thesis will describe lazy evaluation techniques for search trees that allow them to be made fully persistent. A fully persistent search tree supports insertions, deletions, and queries in any version, past or present. The time per query or update is O(log m) where m is the total number of updates, and the space needed is O(1) per update. These bounds are the best possible. Contents