Bounding the Inefficiency of Length-Restricted Prefix Codes

Milidiú, Ruy Luiz; Laber, Eduardo Sany

doi:10.1007/s00453-001-0060-4

Cited by 18 publications

(24 citation statements)

References 20 publications

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“…However, since a Huffman tree can be very deep (height n−1 for a very skewed distribution), this would compromise our time bound. Therefore, we use a an O(log σ)-restricted Huffman tree [30], which yields both the space and time bounds we want.…”

Section: Top-k Queriesmentioning

confidence: 99%

Colored Range Queries and Document Retrieval

Gagie

Navarro

Puglisi

2010

String Processing and Information Retrieval

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Abstract. Colored range queries are a well-studied topic in computational geometry and database research that, in the past decade, have found exciting applications in information retrieval. In this paper we give improved time and space bounds for three important one-dimensional colored range queries -colored range listing, colored range top-k queries and colored range counting -and, thus, new bounds for various document retrieval problems on general collections of sequences. Specifically, we first describe a framework including almost all recent results on colored range listing and document listing, which suggests new combinations of data structures for these problems. For example, we give the fastest compressed data structures for colored range listing and document listing, and an efficient data structure for document listing whose size is bounded in terms of the high-order entropies of the library of documents. We then show how (approximate) colored top-k queries can be reduced to (approximate) range-mode queries on subsequences, yielding the first efficient data structure for this problem. Finally, we show how a modified wavelet tree can support colored range counting in logarithmic time and space that is succinct whenever the number of colors is superpolylogarithmic in the length of the sequence.

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Section: Top-k Queriesmentioning

confidence: 99%

Colored Range Queries and Document Retrieval

Gagie

Navarro

Puglisi

2010

String Processing and Information Retrieval

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“…It follows from Milidiú and Laber's bound [15] that, for any with 0 < < 1/2, there is always a prefix code with maximum codeword length L = log n + log φ (1/ ) + 1 and expected codeword length within an additive…”

Section: Additive Increase In Expected Codeword Lengthmentioning

confidence: 99%

“…Given a constant c > 1, we use Milidiú and Laber's algorithm [15] to build a prefix code with maximum codeword length L = log n + 1/(c − 1) + 1. We call a character's codeword short if it has length at most L/c + 2, and long otherwise.…”

Section: Multiplicative Increase In Expected Codeword Lengthmentioning

confidence: 99%

“…By analysis of the algorithm by Milidiú and Laber [15] we can see that the codeword length of a character in their length-restricted code exceeds the codeword length of the same character in an optimal code by at most 1, and only when the codeword length in the optimal code is at least L − log n − 1 = 1/(c − 1) . Hence, the codeword length of a character encoded with a short codeword exceeds the codeword length of the same character in an optimal code by a factor of at most 1/(c−1) +1 1/(c−1) ≤ c. Every infrequent character is encoded with a codeword of length L + 1.…”

Section: Multiplicative Increase In Expected Codeword Lengthmentioning

confidence: 99%

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Fast and Compact Prefix Codes

Gagie

Navarro

Nekrich

2010

SOFSEM 2010: Theory and Practice of Computer Science

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Abstract. It is well-known that, given a probability distribution over n characters, in the worst case it takes Θ(n log n) bits to store a prefix code with minimum expected codeword length. However, in this paper we first show that, for any with 0 < < 1/2 and 1/ = O(polylog(n)), it takes O(n log log(1/ )) bits to store a prefix code with expected codeword length within an additive of the minimum. We then show that, for any constant c > 1, it takes O n 1/c log n bits to store a prefix code with expected codeword length at most c times the minimum. In both cases, our data structures allow us to encode and decode any character in O(1) time.

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“…Finding fast algorithms for computing optimal depth constrained binary trees (without the alphabetic constraint) is known to be a hard problem and good approximate solutions are appearing only now [18], [12], [19], almost 40 years after the original Huffman algorithm. Imposing the alphabetic constraint renders the problem even harder [20], [21], [22], [23].…”

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confidence: 99%

Near-optimal routing lookups with bounded worst case performance

Gupta

Prabhakar

Boyd

Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer A

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Abstract-The problem of route address lookup has received much attention recently and several algorithms and data structures for performing address lookups at high speeds have been proposed. In this paper we consider one such data structure -a binary search tree built on the intervals created by the routing table prefixes. We wish to exploit the difference in the probabilities with which the various leaves of the tree (where the intervals are stored) are accessed by incoming packets in order to speedup the lookup process. More precisely, we seek an answer to the question "How can the search tree be drawn so as to minimize the average packet lookup time while keeping the worst-case lookup time within a fixed bound?" We use ideas from information theory to derive efficient algorithms for computing near-optimal routing lookup trees. Finally, we consider the practicality of our algorithms through analysis and simulation.

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Bounding the Inefficiency of Length-Restricted Prefix Codes

Cited by 18 publications

References 20 publications

Colored Range Queries and Document Retrieval

Colored Range Queries and Document Retrieval

Fast and Compact Prefix Codes

Near-optimal routing lookups with bounded worst case performance

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