Search results for "Data structures"
showing 10 items of 258 documents
String attractors and combinatorics on words
2019
The notion of \emph{string attractor} has recently been introduced in [Prezza, 2017] and studied in [Kempa and Prezza, 2018] to provide a unifying framework for known dictionary-based compressors. A string attractor for a word $w=w[1]w[2]\cdots w[n]$ is a subset $\Gamma$ of the positions $\{1,\ldots,n\}$, such that all distinct factors of $w$ have an occurrence crossing at least one of the elements of $\Gamma$. While finding the smallest string attractor for a word is a NP-complete problem, it has been proved in [Kempa and Prezza, 2018] that dictionary compressors can be interpreted as algorithms approximating the smallest string attractor for a given word. In this paper we explore the noti…
Large-scale compression of genomic sequence databases with the Burrows-Wheeler transform
2012
Motivation The Burrows-Wheeler transform (BWT) is the foundation of many algorithms for compression and indexing of text data, but the cost of computing the BWT of very large string collections has prevented these techniques from being widely applied to the large sets of sequences often encountered as the outcome of DNA sequencing experiments. In previous work, we presented a novel algorithm that allows the BWT of human genome scale data to be computed on very moderate hardware, thus enabling us to investigate the BWT as a tool for the compression of such datasets. Results We first used simulated reads to explore the relationship between the level of compression and the error rate, the leng…
Alignment-free Genomic Analysis via a Big Data Spark Platform
2021
Abstract Motivation Alignment-free distance and similarity functions (AF functions, for short) are a well-established alternative to pairwise and multiple sequence alignments for many genomic, metagenomic and epigenomic tasks. Due to data-intensive applications, the computation of AF functions is a Big Data problem, with the recent literature indicating that the development of fast and scalable algorithms computing AF functions is a high-priority task. Somewhat surprisingly, despite the increasing popularity of Big Data technologies in computational biology, the development of a Big Data platform for those tasks has not been pursued, possibly due to its complexity. Results We fill this impo…
Binary jumbled string matching for highly run-length compressible texts
2012
The Binary Jumbled String Matching problem is defined as: Given a string $s$ over $\{a,b\}$ of length $n$ and a query $(x,y)$, with $x,y$ non-negative integers, decide whether $s$ has a substring $t$ with exactly $x$ $a$'s and $y$ $b$'s. Previous solutions created an index of size O(n) in a pre-processing step, which was then used to answer queries in constant time. The fastest algorithms for construction of this index have running time $O(n^2/\log n)$ [Burcsi et al., FUN 2010; Moosa and Rahman, IPL 2010], or $O(n^2/\log^2 n)$ in the word-RAM model [Moosa and Rahman, JDA 2012]. We propose an index constructed directly from the run-length encoding of $s$. The construction time of our index i…
Time and space efficient quantum algorithms for detecting cycles and testing bipartiteness
2016
We study space and time efficient quantum algorithms for two graph problems -- deciding whether an $n$-vertex graph is a forest, and whether it is bipartite. Via a reduction to the s-t connectivity problem, we describe quantum algorithms for deciding both properties in $\tilde{O}(n^{3/2})$ time and using $O(\log n)$ classical and quantum bits of storage in the adjacency matrix model. We then present quantum algorithms for deciding the two properties in the adjacency array model, which run in time $\tilde{O}(n\sqrt{d_m})$ and also require $O(\log n)$ space, where $d_m$ is the maximum degree of any vertex in the input graph.
Word assembly through minimal forbidden words
2006
AbstractWe give a linear-time algorithm to reconstruct a finite word w over a finite alphabet A of constant size starting from a finite set of factors of w verifying a suitable hypothesis. We use combinatorics techniques based on the minimal forbidden words, which have been introduced in previous papers. This improves a previous algorithm which worked under the assumption of stronger hypothesis.
From Nerode's congruence to Suffix Automata with mismatches
2009
AbstractIn this paper we focus on the minimal deterministic finite automaton Sk that recognizes the set of suffixes of a word w up to k errors. As first result we give a characterization of the Nerode’s right-invariant congruence that is associated with Sk. This result generalizes the classical characterization described in [A. Blumer, J. Blumer, D. Haussler, A. Ehrenfeucht, M. Chen, J. Seiferas, The smallest automaton recognizing the subwords of a text, Theoretical Computer Science, 40, 1985, 31–55]. As second result we present an algorithm that makes use of Sk to accept in an efficient way the language of all suffixes of w up to k errors in every window of size r of a text, where r is the…
Minimal forbidden patterns of multi-dimensional shifts
2005
We study whether the entropy (or growth rate) of minimal forbidden patterns of symbolic dynamical shifts of dimension 2 or more, is a conjugacy invariant. We prove that the entropy of minimal forbidden patterns is a conjugacy invariant for uniformly semi-strongly irreducible shifts. We prove a weaker invariant in the general case.
A walk on sunset boulevard
2016
A walk on sunset boulevard can teach us about transcendental functions associated to Feynman diagrams. On this guided tour we will see multiple polylogarithms, differential equations and elliptic curves. A highlight of the tour will be the generalisation of the polylogarithms to the elliptic setting and the all-order solution for the sunset integral in the equal mass case.
Standard Vs Uniform Binary Search and Their Variants in Learned Static Indexing: The Case of the Searching on Sorted Data Benchmarking Software Platf…
2023
Learned Indexes are a novel approach to search in a sorted table. A model is used to predict an interval in which to search into and a Binary Search routine is used to finalize the search. They are quite effective. For the final stage, usually, the lower_bound routine of the Standard C++ library is used, although this is more of a natural choice rather than a requirement. However, recent studies, that do not use Machine Learning predictions, indicate that other implementations of Binary Search or variants, namely k-ary Search, are better suited to take advantage of the features offered by modern computer architectures. With the use of the Searching on Sorted Sets SOSD Learned Indexing bench…