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The grid file: an adaptable, symmetric multikey file structure
 In Trends in Information Processing Systems, Proc. 3rd ECZ Conference, A. Duijvestijn and P. Lockemann, Eds., Lecture Notes in Computer Science 123
, 1981
"... Traditional file structures that provide multikey access to records, for example, inverted files, are extensions of file structures originally designed for singlekey access. They manifest various deficiencies in particular for multikey access to highly dynamic files. We study the dynamic aspects of ..."
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Cited by 398 (4 self)
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Traditional file structures that provide multikey access to records, for example, inverted files, are extensions of file structures originally designed for singlekey access. They manifest various deficiencies in particular for multikey access to highly dynamic files. We study the dynamic aspects of tile structures that treat all keys symmetrically, that is, file structures which avoid the distinction between primary and secondary keys. We start from a bitmap approach and treat the problem of file design as one of data compression of a large sparse matrix. This leads to the notions of a grid partition of the search space and of a grid directory, which are the keys to a dynamic file structure called the grid file. This tile system adapts gracefully to its contents under insertions and deletions, and thus achieves an upper hound of two disk accesses for single record retrieval; it also handles range queries and partially specified queries efficiently. We discuss in detail the design decisions that led to the grid file, present simulation results of its behavior, and compare it to other multikey access file structures.
Selfadjusting binary search trees
, 1985
"... The splay tree, a selfadjusting form of binary search tree, is developed and analyzed. The binary search tree is a data structure for representing tables and lists so that accessing, inserting, and deleting items is easy. On an nnode splay tree, all the standard search tree operations have an am ..."
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Cited by 384 (16 self)
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The splay tree, a selfadjusting form of binary search tree, is developed and analyzed. The binary search tree is a data structure for representing tables and lists so that accessing, inserting, and deleting items is easy. On an nnode splay tree, all the standard search tree operations have an amortized time bound of O(log n) per operation, where by “amortized time ” is meant the time per operation averaged over a worstcase sequence of operations. Thus splay trees are as efficient as balanced trees when total running time is the measure of interest. In addition, for sufficiently long access sequences, splay trees are as efficient, to within a constant factor, as static optimum search trees. The efftciency of splay trees comes not from an explicit structural constraint, as with balanced trees, but from applying a simple restructuring heuristic, called splaying, whenever the tree is accessed. Extensions of splaying give simplified forms of two other data structures: lexicographic or multidimensional search trees and link/ cut trees.
A General Technique for Managing Strings in ComparisonDriven Data Structures
"... Abstract. This paper presents a general technique for optimally transforming any dynamic data structure D that operates on atomic and indivisible keys by constanttime comparisons, into a data structure D ′ that handles unboundedlength keys whose comparison cost is not a constant. 1 ..."
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Abstract. This paper presents a general technique for optimally transforming any dynamic data structure D that operates on atomic and indivisible keys by constanttime comparisons, into a data structure D ′ that handles unboundedlength keys whose comparison cost is not a constant. 1
Simple Algorithms For The Online Multidimensional Dictionary and Related Problems
, 1998
"... The online multidimensional dictionary problem consists of executing online any sequence of the following operations: INSERT(p), DELETE(p) and MEMBERSHIP(p), where p is any (ordered) dtuple (or string with d elements, or points in dspace where the dimensions have been ordered). We introduce a cl ..."
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The online multidimensional dictionary problem consists of executing online any sequence of the following operations: INSERT(p), DELETE(p) and MEMBERSHIP(p), where p is any (ordered) dtuple (or string with d elements, or points in dspace where the dimensions have been ordered). We introduce a clean structure based on balanced binary search trees, which we call multidimensional balanced binary search trees, to represent the set of dtuples. We present algorithms for each of the above operations that take O(d + log n) time, where n is the current number of dtuples in the set, and each INSERT and DELETE operation requires no more than a constant number of rotations. Our structure requires dn words to represent the input, plus O(n) pointers and data indicating the first component where pairs of dtuples differ. This information, which can be easily updated, enables us to test for MEMBERSHIP efficiently. Other operations that can be performed efficiently in our multidimensional balanc...