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Related papers: Low-Memory Adaptive Prefix Coding

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Efficient optimal prefix coding has long been accomplished via the Huffman algorithm. However, there is still room for improvement and exploration regarding variants of the Huffman problem. Length-limited Huffman coding, useful for many…

Information Theory · Computer Science 2007-07-13 Michael B. Baer

Given a string $S$ of length $n$, the classic string indexing problem is to preprocess $S$ into a compact data structure that supports efficient subsequent pattern queries. In the \emph{deterministic} variant the goal is to solve the string…

Data Structures and Algorithms · Computer Science 2016-12-07 Philip Bille , Inge Li Gørtz , Frederik Rye Skjoldjensen

Adaptive variable-length codes associate a variable-length codeword to the symbol being encoded depending on the previous symbols in the input string. This class of codes has been recently presented in [Dragos Trinca, arXiv:cs.DS/0505007]…

Data Structures and Algorithms · Computer Science 2007-05-23 Dragos Trinca

We study the problem of supporting queries on a string $S$ of length $n$ within a space bounded by the size $\gamma$ of a string attractor for $S$. Recent works showed that random access on $S$ can be supported in optimal…

Data Structures and Algorithms · Computer Science 2018-12-24 Nicola Prezza

In this paper, we study the problem of designing prefix-free encoding schemes having minimum average code length that can be decoded efficiently under a decode cost model that captures memory hierarchy induced cost functions. We also study…

Data Structures and Algorithms · Computer Science 2021-10-22 Shashwat Banchhor , Rishikesh Gajjala , Yogish Sabharwal , Sandeep Sen

We present an algorithm which computes the Lempel-Ziv factorization of a word $W$ of length $n$ on an alphabet $\Sigma$ of size $\sigma$ online in the following sense: it reads $W$ starting from the left, and, after reading each $r =…

Data Structures and Algorithms · Computer Science 2012-12-03 Tatiana Starikovskaya

We describe an algorithm computing an optimal prefix free code for $n$ unsorted positive weights in time within $O(n(1+\lg \alpha))\subseteq O(n\lg n)$, where the alternation $\alpha\in[1..n-1]$ measures the amount of sorting required by…

Data Structures and Algorithms · Computer Science 2016-02-02 Jérémy Barbay

We present a compressed representation of tries based on top tree compression [ICALP 2013] that works on a standard, comparison-based, pointer machine model of computation and supports efficient prefix search queries. Namely, we show how to…

Data Structures and Algorithms · Computer Science 2019-09-23 Philip Bille , Inge Li Gørtz , Paweł Gawrychowski , Gad M. Landau , Oren Weimann

Given a pattern $P$ and a text $T$, both strings over a binary alphabet, the binary jumbled string matching problem consists in telling whether any permutation of $P$ occurs in $T$. The indexed version of this problem, i.e., preprocessing a…

Data Structures and Algorithms · Computer Science 2013-05-09 Emanuele Giaquinta , Szymon Grabowski

It is widely assumed that $O(m+\lg \sigma)$ is the best one can do for finding a pattern of length $m$ in a compacted trie storing strings over an alphabet of size $\sigma$, if one insists on linear-size data structures and deterministic…

Data Structures and Algorithms · Computer Science 2013-02-15 Johannes Fischer , Pawel Gawrychowski

Given a string of length $n$ that is composed of $r$ runs of letters from the alphabet $\{0,1,\ldots,\sigma{-}1\}$ such that $2 \le \sigma \le r$, we describe a data structure that, provided $r \le n / \log^{\omega(1)} n$, stores the string…

Data Structures and Algorithms · Computer Science 2018-02-27 José Fuentes-Sepúlveda , Juha Kärkkäinen , Dmitry Kosolobov , Simon J. Puglisi

We describe an algorithm computing an optimal prefix free code from $N$ unsorted positive integer weights in time linear in the number of machine words holding those weights. This algorithm takes advantage of common non-algebraic…

Data Structures and Algorithms · Computer Science 2017-03-02 Jérémy Barbay

In prefix coding over an infinite alphabet, methods that consider specific distributions generally consider those that decline more quickly than a power law (e.g., Golomb coding). Particular power-law distributions, however, model many…

Information Theory · Computer Science 2009-03-06 Michael B. Baer

Adaptive coding faces the following problem: given a collection of source classes such that each class in the collection has non-trivial minimax redundancy rate, can we design a single code which is asymptotically minimax over each class in…

Information Theory · Computer Science 2016-09-02 Anna Ben-Hamou , Stephane Boucheron , Elisabeth Gassiat

Let two static sequences of strings $P$ and $S$, representing prefix and suffix conditions respectively, be given as input for preprocessing. For the query, let two positive integers $k_1$ and $k_2$ be given, as well as a string $T$ given…

Data Structures and Algorithms · Computer Science 2022-11-01 Laurentius Leonard , Shunsuke Inenaga , Hideo Bannai , Takuya Mieno

We consider the problem of finding repetitive structures and inherent patterns in a given string $\s{s}$ of length $n$ over a finite totally ordered alphabet. A border $\s{u}$ of a string $\s{s}$ is both a prefix and a suffix of $\s{s}$…

Data Structures and Algorithms · Computer Science 2015-06-24 Ali Alatabbi , Jacqueline W. Daykin , M. Sohel Rahman

Packing several characters into one computer word is a simple and natural way to compress the representation of a string and to speed up its processing. Exploiting this idea, we propose an index for a packed string, based on a {\em sparse…

Data Structures and Algorithms · Computer Science 2015-03-19 Roman Kolpakov , Gregory Kucherov , Tatiana Starikovskaya

Given $d$ strings over the alphabet $\{0,1,\ldots,\sigma{-}1\}$, the classical Aho--Corasick data structure allows us to find all $occ$ occurrences of the strings in any text $T$ in $O(|T| + occ)$ time using $O(m\log m)$ bits of space,…

Data Structures and Algorithms · Computer Science 2019-04-02 Dmitry Kosolobov , Nikita Sivukhin

We present a new on-line algorithm for computing the Lempel-Ziv factorization of a string that runs in $O(N\log N)$ time and uses only $O(N\log\sigma)$ bits of working space, where $N$ is the length of the string and $\sigma$ is the size of…

Data Structures and Algorithms · Computer Science 2013-05-28 Jun'ichi Yamamoto , Tomohiro I , Hideo Bannai , Shunsuke Inenaga , Masayuki Takeda

We consider the Abelian longest common factor problem in two scenarios: when input strings are uncompressed and are of size $n$, and when the input strings are run-length encoded and their compressed representations have size at most $m$.…

Data Structures and Algorithms · Computer Science 2018-04-19 Szymon Grabowski , Tomasz Kociumaka , Jakub Radoszewski