Searching for authors named "Travis Gagie" – sorted by Relevance.
11 documents found, showing 1 through 10.
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Sorting a Low-Entropy Sequence
- …We give the first sorting algorithm with bounds in terms of higher-order entropies: let S be a sequence of length m containing n distinct elements and let H # (S) be the #th-order empirical entropy of S, log n # O(m); our algorithm sorts S using (H # (S) + O(1))m comparisons.…
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Compressing Probability Distributions
- …this paper we measure fidelity using relative entropy because, in the asymmetric communication example above, the relative entropy is roughly how many more bits we expect the client to send with the server's help than if it knew the distribution itself. Let P = p 1 , . . . , p n and Q = q 1 , . . . …
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Dynamic Asymmetric Communication
- …In Adler and Maggs' asymmetric communication problem, a server with high bandwidth tries to help clients with low bandwidth send it messages. We give four new asymmetric communication protocols and show they are robust with respect to changes in the messages' distribution.…
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Dynamic Length-Restricted Coding
- …Suppose that $S$ is a string of length $m$ drawn from an alphabet of $n$ characters, $d$ of which occur in $S$. Let $P$ be the relative frequency distribution of characters in $S$. We present a new algorithm for dynamic coding that uses at most \(\lceil \lg n \rceil 1\) bits to encode each character…
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Dynamic Shannon Coding
- …We present a new algorithm for dynamic prefixfree coding, based on Shannon coding. We give a simple analysis and prove a better upper bound on the length of the encoding produced than the corresponding bound for dynamic Huffman coding. We show how our algorithm can be modified for efficient length-r…
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Large Alphabets and Incompressibility
- …We briefly survey some concepts related to empirical entropy --- normal numbers, de Bruijn sequences and Markov processes --- and investigate how well it approximates Kolmogorov complexity. Our results suggest #th-order empirical entropy stops being a reasonable complexity metric for almost all st…
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Move-to-Front, Distance Coding, and Inversion Frequencies Revisited ∗
- …Move-to-Front, Distance Coding and Inversion Frequencies are three somewhat related techniques used to process the output of the Burrows-Wheeler Transform. In this paper we analyze these techniques from the point of view of how effective they are in the task of compressing low-entropy strings, that …
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A Note On Sequence Prediction
- …We show sequences are predictable, in a certain sense, if they are su#ciently long and contain relatively few distinct elements. We define a statistic P # (S) that measures how well any function predicts a sequence S using only contexts of length #. If a function's success rate predicting S is at le…
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Dynamic Asymmetric Communication
- …We present four new asymmetric communication protocols, with which a server with high bandwidth can help clients with low bandwidth send it messages. Three of our protocols are the first to use only a single round of communication for each message. Unlike previous authors, we do not assume the s…
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Information Processing Letters 95 (2005) 418--421
- …this paper we show how, given one binary search tree T , we can construct another binary search tree E-mail address: travis@cs.toronto.edu (T. Gagie)…
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