File structures using hashing functions

Coffman, E. G.; Eve, J.

doi:10.1145/362686.362693

Cited by 97 publications

(51 citation statements)

References 3 publications

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“…The advantage of digital search trees is a much better worst-case performance. Furthermore it can be shown that the average-case performance is asymptotically optimal (see [CE74,FS86]). …”

Section: The Tree Classesmentioning

confidence: 99%

On the shape of the fringe of various types of random trees

Drmota

Gittenberger

Panholzer

et al. 2008

Math Methods in App Sciences

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Abstract. We analyze a fringe tree parameter w in a variety of settings, utilizing a variety of methods from the analysis of algorithms and data structures.Given a tree t and one of its leaves a, the w(t, a) parameter denotes the number of internal nodes in the subtree rooted at a's father. The closely-related w(t, a) parameter denotes the number of leaves, excluding a, in the subtree rooted at a's father. We define the cumulative w parameter as W(t) = a w(t, a), i.e., as the sum of w(t, a) over all leaves a of t. The w parameter not only plays an important rôle in the analysis of the Lempel-Ziv '77 data compression algorithm, but it is captivating from a combinatorial viewpoint too.In this report, we determine the asymptotic behavior of the w and W parameters on a variety of types of trees. In particular, we analyze simply generated trees, recursive trees, binary search trees, digital search trees, tries and Patricia tries.The final section of this report briefly summarizes and improves the previously known results about the w parameter's behavior on tries and suffix trees, originally published in one author's thesis (see [War05]This survey of new results about the w parameter is very instructive since a variety of different combinatorial methods are used in tandem to carry out the analysis.

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“…The advantage of digital search trees is a much better worst-case performance. Furthermore it can be shown that the average-case performance is asymptotically optimal (see [CE74,FS86]). …”

Section: The Tree Classesmentioning

confidence: 99%

On the shape of the fringe of various types of random trees

Drmota

Gittenberger

Panholzer

et al. 2008

Math Methods in App Sciences

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“…A data structure of Coffman and Eve [7], called a sequence hash tree, was designed for the problem of implementing hash tables (dictionaries) whose keys are strings. It consists of a trie for indexing into the table.…”

Section: Sequence Hash Treesmentioning

confidence: 99%

Contracted Suffix Trees: A Simple and Dynamic Text Indexing Data Structure

Ehrenfeucht

McConnell

Woo

2009

Combinatorial Pattern Matching

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Abstract. We address the problem of finding the locations of all instances of a string P in a text T , where of T is allowed to facilitate the queries. Previous data structures for this problem include the suffix tree, the suffix array, and the compact DAWG. We modify a data structure called a sequence tree, which was proposed by Coffman and Eve for hashing, and adapt it to the new problem. We can then produce a list of k occurrences of any string P in T in O(||P || + k) time. Because of properties shared by suffixes of a text that are not shared by arbitrary hash keys, we can build the structure in O(||T ||) time, which is much faster than Coffman and Eve's algorithm. These bounds are as good as those for the suffix tree, suffix array, and the compact DAWG. The advantages are the elementary nature of some of the algorithms for constructing and using the data structure and the asymptotic bounds we can give for updating the data structure when the text is edited.

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“…Attempts in this direction include patricia trees (Morrison, 1968), and digital search trees (Coffman and Eve, 1970;Konheim and Newman, 1973). In both cases, we have H n log n → 1 log 1 max 1≤i≤k pi in probability (Pittel, 1985).…”

Section: Digital Search Treesmentioning

confidence: 99%

The height of increasing trees

Broutin

Devroye

McLeish

et al. 2008

Random Struct Algorithms

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We extend results about heights of random trees (Devroye, 1986(Devroye, , 1987(Devroye, , 1998b. In this paper, a general split tree model is considered in which the normalized subtree sizes of nodes converge in distribution. The height of these trees is shown to be in probability asymptotic to c log n for some constant c. We apply our results to obtain a law of large numbers for the height of all polynomial varieties of increasing trees (Bergeron et al., 1992).

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File structures using hashing functions

Cited by 97 publications

References 3 publications

On the shape of the fringe of various types of random trees

On the shape of the fringe of various types of random trees

Contracted Suffix Trees: A Simple and Dynamic Text Indexing Data Structure

The height of increasing trees

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