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We give three different computations of the total number of runs of length $i$ in binary $n$-strings, and we discuss the connection of this problem with the compositions of $n$.

Combinatorics · Mathematics 2023-02-28 Félix Balado , Guénolé C. M. Silvestre

We propose an incremental strategy for learning hash functions with kernels for large-scale image search. Our method is based on a two-stage classification framework that treats binary codes as intermediate variables between the feature…

Computer Vision and Pattern Recognition · Computer Science 2016-06-10 Bahadir Ozdemir , Mahyar Najibi , Larry S. Davis

Online hashing methods are efficient in learning the hash functions from the streaming data. However, when the hash functions change, the binary codes for the database have to be recomputed to guarantee the retrieval accuracy. Recomputing…

Data Structures and Algorithms · Computer Science 2019-12-05 Zhenyu Weng , Yuesheng Zhu

Mastermind is in essence a search problem in which a string of symbols that is kept secret must be found by sequentially playing strings that use the same alphabet, and using the responses that indicate how close are those other strings to…

Neural and Evolutionary Computing · Computer Science 2012-07-06 J. J. Merelo , Antonio M. Mora , Carlos Cotta , Thomas P. Runarsson

A two-dimensional string is simply a two-dimensional array. We continue the study of the combinatorial properties of repetitions in such strings over the binary alphabet, namely the number of distinct tandems, distinct quartics, and runs.…

Formal Languages and Automata Theory · Computer Science 2021-06-01 Paweł Gawrychowski , Samah Ghazawi , Gad M. Landau

A novel fast recursive coding technique is proposed. It operates with only integer values not longer 8 bits and is multiplication free. Recursion the algorithm is based on indirectly provides rather effective coding of symbols for very…

Information Theory · Computer Science 2007-08-22 Nikolay Ponomarenko , Vladimir Lukin , Karen Egiazarian , Jaakko Astola , Boris Y Ryabko

Sorting and hashing are two completely different concepts in computer science, and appear mutually exclusive to one another. Hashing is a search method using the data as a key to map to the location within memory, and is used for rapid…

Data Structures and Algorithms · Computer Science 2007-05-23 William F. Gilreath

Exact string matching has been a fundamental problem in computer science for decades because of many practical applications. Some are related to common procedures, such as searching in files and text editors, or, more recently, to more…

Data Structures and Algorithms · Computer Science 2019-07-29 Konstantinos F. Xylogiannopoulos

Fast similarity search is a key component in large-scale information retrieval, where semantic hashing has become a popular strategy for representing documents as binary hash codes. Recent advances in this area have been obtained through…

Information Retrieval · Computer Science 2019-06-04 Casper Hansen , Christian Hansen , Jakob Grue Simonsen , Stephen Alstrup , Christina Lioma

Hashing has recently sparked a great revolution in cross-modal retrieval because of its low storage cost and high query speed. Recent cross-modal hashing methods often learn unified or equal-length hash codes to represent the multi-modal…

Computer Vision and Pattern Recognition · Computer Science 2019-09-13 Xin Liu , Zhikai Hu , Haibin Ling , Yiu-ming Cheung

The (bounded) hairpin completion and its iterated versions are operations on formal lan- guages which have been inspired by the hairpin formation in DNA-biochemistry. The paper answers two questions asked in the literature about the…

Formal Languages and Automata Theory · Computer Science 2015-03-17 Steffen Kopecki

Strings form a fundamental data type in computer systems. String searching has been extensively studied since the inception of computer science. Increasingly many applications have to deal with imprecise strings or strings with fuzzy…

Databases · Computer Science 2015-09-30 Sharma V. Thankachan , Manish Patil , Rahul Shah , Sudip Biswas

The first two authors have shown [KK99,KK00] that the sum the exponent (and thus the number) of maximal repetitions of exponent at least 2 (also called runs) is linear in the length of the word. The exponent 2 in the definition of a run may…

Discrete Mathematics · Computer Science 2009-06-26 Roman Kolpakov , Gregory Kucherov , Pascal Ochem

Upper bounds on the maximum number of codewords in a binary code of a given length and minimum Hamming distance are considered. New bounds are derived by a combination of linear programming and counting arguments. Some of these bounds…

Information Theory · Computer Science 2007-07-13 Beniamin Mounits , Tuvi Etzion , Simon Litsyn

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

In recent years, the distinctive advancement of handling huge data promotes the evolution of ubiquitous computing and analysis technologies. With the constantly upward system burden and computational complexity, adaptive coding has been a…

Computer Vision and Pattern Recognition · Computer Science 2018-10-16 Miao Cheng , Ah Chung Tsoi

We introduce a novel dependency parser, the hexatagger, that constructs dependency trees by tagging the words in a sentence with elements from a finite set of possible tags. In contrast to many approaches to dependency parsing, our approach…

Computation and Language · Computer Science 2023-08-01 Afra Amini , Tianyu Liu , Ryan Cotterell

Hash tables are ubiquitous, and the choice of hash function, which maps a key to a bucket, is key to their performance. We argue that the predominant approach of fixing the hash function for the lifetime of the hash table is suboptimal and…

Data Structures and Algorithms · Computer Science 2026-02-09 Gábor Melis

Two objects are independent if they do not affect each other. Independence is well-understood in classical information theory, but less in algorithmic information theory. Working in the framework of algorithmic information theory, the paper…

Information Theory · Computer Science 2008-02-05 Cristian Calude , Marius Zimand

We show that linear probing requires 5-independent hash functions for expected constant-time performance, matching an upper bound of [Pagh et al. STOC'07]. More precisely, we construct a 4-independent hash functions yielding expected…

Data Structures and Algorithms · Computer Science 2014-12-25 Mikkel Thorup
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