Application of splay trees to data compression

Jones, Douglas R.

doi:10.1145/63030.63036

Cited by 76 publications

(34 citation statements)

References 9 publications

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“…Jones [3] uses splay trees for handling cumulative frequencies. A splay tree is a self-balancing binary search tree with the additional property that recently accessed elements are quick to access again.…”

Section: Mtf Array Moffat's Heap Splay Treementioning

confidence: 99%

Implementing a Novel Data Structure for Maintaining Cumulative Frequency of Symbols

Doshi¹,

Gandhi²

2012

IJCA

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A new data structure, namely "cumulative frequency matrix (CFM)", is proposed here for maintaining cumulative frequencies. For an order-0 model having 256 symbols, CFM is a 2-D array of 16 rows and 16 columns. Two nibbles, say L for left and R for right, of a byte symbol represents row and column dimensions respectively. Matrix element (L, R) represents cumulative frequency of symbol with right nibble as R among symbols with left nibble as L. Within row, it stores cumulative frequency of symbols with right nibble varying from 0 to 15. Adaptive arithmetic coding is a lossless data compression method. It needs to update cumulative frequencies at runtime. Various algorithms for maintaining cumulative frequencies, computing cumulative frequency interval etc. are discussed here. Practical implementation shows that proposed data structure is simpler as well as efficient as compared to other data structures in use.

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Section: Mtf Array Moffat's Heap Splay Treementioning

confidence: 99%

Implementing a Novel Data Structure for Maintaining Cumulative Frequency of Symbols

Doshi¹,

Gandhi²

2012

IJCA

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“…Splaying has found application in areas where amortised performance is important, including in data compression [7,10], sorting [14], and index construction [22,24]. In addition, extended n-ary splay trees and variants have been proposed and compared to static n-ary trees, with similar amortised performance [12,19].…”

Section: Splay Treesmentioning

confidence: 99%

Self‐adjusting trees in practice for large text collections

2001

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Splay and randomised search trees are self-balancing binary tree structures with little or no space overhead compared to a standard binary search tree. Both trees are intended for use in applications where node accesses are skewed, for example in gathering the distinct words in a large text collection for index construction. We investigate the efficiency of these trees for such vocabulary accumulation. Surprisingly, unmodified splaying and randomised search trees are on average around 25% slower than using a standard binary tree. We investigate heuristics to limit splay tree reorganisation costs and show their effectiveness in practice. In particular, a periodic rotation scheme improves the speed of splaying by 27%, while other proposed heuristics are less effective. We also report the performance of efficient bit-wise hashing and red-black trees for comparison.

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“…That is why the problem of constructing high-speed codes for large alphabets has attracted great attention by researches. Important results have been obtained by Moffat, Turpin [8,10,9,12,19,11] and others [3,6,7,14,15,2,18].…”

mentioning

confidence: 94%

“…The time of an obvious (or naive) method of updating the cumulative probabilities is proportional to the alphabet size N . Jones [3] and Ryabko [14] have independently suggested two different algorithms, which perform all the necessary transitions between individual and cumulative probabilities in O(log N ) operations under (log N + τ )-bit words, where τ is a constant depending on the redundancy required, N is the alphabet size.…”

mentioning

confidence: 99%

Fast codes for large alphabets

Ryabko

Astola

Егиазарян

2003

Communications in Information and Systems

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Abstract. We address the problem of constructing a fast lossless code in the case when the source alphabet is large. The main idea of the new scheme may be described as follows. We group letters with small probabilities in subsets (acting as super letters) and use time consuming coding for these subsets only, whereas letters in the subsets have the same code length and therefore can be coded fast. The described scheme can be applied to sources with known and unknown statistics.

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Application of splay trees to data compression

Cited by 76 publications

References 9 publications

Implementing a Novel Data Structure for Maintaining Cumulative Frequency of Symbols

Implementing a Novel Data Structure for Maintaining Cumulative Frequency of Symbols

Self‐adjusting trees in practice for large text collections

Fast codes for large alphabets

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