Implementation of parallel algorithm for run of k-local tree automata

Tato práce se zabývá k-lokálními deterministickými konečnými stromovými automaty (DKSA), které hrají důležitou roli při hledání vzorů ve stromových strukturách. Existuje pracovně optimální paralelní algoritmus pro běh k-lokálních DKSA na výpočetním modelu EREW PRAM. Tento algoritmus bude implementován, experimentálně změřen a porovnán se sekvenčním algoritmem v této práci.This thesis deals with k-local deterministic finite tree automata (DFTA) which are important for tree pattern matching. There exists a work-optimal parallel algorithm for a run of k-local DFTA on EREW PRAM. This algorithm will be implemented, experimentally measured and compared with the sequential algorithm in this thesis

NC Algorithms for Computing a Perfect Matching and a Maximum Flow in One-Crossing-Minor-Free Graphs

In 1988, Vazirani gave an NC algorithm for computing the number of perfect matchings in $K_{3,3}$-minor-free graphs by building on Kasteleyn's scheme for planar graphs, and stated that this "opens up the possibility of obtaining an NC algorithm for finding a perfect matching in $K_{3,3}$-free graphs." In this paper, we finally settle this 30-year-old open problem. Building on recent NC algorithms for planar and bounded-genus perfect matching by Anari and Vazirani and later by Sankowski, we obtain NC algorithms for perfect matching in any minor-closed graph family that forbids a one-crossing graph. This family includes several well-studied graph families including the $K_{3,3}$-minor-free graphs and $K_5$-minor-free graphs. Graphs in these families not only have unbounded genus, but can have genus as high as $O(n)$. Our method applies as well to several other problems related to perfect matching. In particular, we obtain NC algorithms for the following problems in any family of graphs (or networks) with a one-crossing forbidden minor: $\bullet$ Determining whether a given graph has a perfect matching and if so, finding one. $\bullet$ Finding a minimum weight perfect matching in the graph, assuming that the edge weights are polynomially bounded. $\bullet$ Finding a maximum $st$-flow in the network, with arbitrary capacities. The main new idea enabling our results is the definition and use of matching-mimicking networks, small replacement networks that behave the same, with respect to matching problems involving a fixed set of terminals, as the larger network they replace.Comment: 21 pages, 6 figure

On the Benefit of Merging Suffix Array Intervals for Parallel Pattern Matching

We present parallel algorithms for exact and approximate pattern matching with suffix arrays, using a CREW-PRAM with $p$ processors. Given a static text of length $n$, we first show how to compute the suffix array interval of a given pattern of length $m$ in $O(\frac{m}{p}+ \lg p + \lg\lg p\cdot\lg\lg n)$ time for $p \le m$. For approximate pattern matching with $k$ differences or mismatches, we show how to compute all occurrences of a given pattern in $O(\frac{m^k\sigma^k}{p}\max\left(k,\lg\lg n\right)\!+\!(1+\frac{m}{p}) \lg p\cdot \lg\lg n + \text{occ})$ time, where $\sigma$ is the size of the alphabet and $p \le \sigma^k m^k$. The workhorse of our algorithms is a data structure for merging suffix array intervals quickly: Given the suffix array intervals for two patterns $P$ and $P'$, we present a data structure for computing the interval of $PP'$ in $O(\lg\lg n)$ sequential time, or in $O(1+\lg_p\lg n)$ parallel time. All our data structures are of size $O(n)$ bits (in addition to the suffix array)

Linear Compressed Pattern Matching for Polynomial Rewriting (Extended Abstract)

This paper is an extended abstract of an analysis of term rewriting where the terms in the rewrite rules as well as the term to be rewritten are compressed by a singleton tree grammar (STG). This form of compression is more general than node sharing or representing terms as dags since also partial trees (contexts) can be shared in the compression. In the first part efficient but complex algorithms for detecting applicability of a rewrite rule under STG-compression are constructed and analyzed. The second part applies these results to term rewriting sequences. The main result for submatching is that finding a redex of a left-linear rule can be performed in polynomial time under STG-compression. The main implications for rewriting and (single-position or parallel) rewriting steps are: (i) under STG-compression, n rewriting steps can be performed in nondeterministic polynomial time. (ii) under STG-compression and for left-linear rewrite rules a sequence of n rewriting steps can be performed in polynomial time, and (iii) for compressed rewrite rules where the left hand sides are either DAG-compressed or ground and STG-compressed, and an STG-compressed target term, n rewriting steps can be performed in polynomial time.Comment: In Proceedings TERMGRAPH 2013, arXiv:1302.599

Prospects and limitations of full-text index structures in genome analysis

The combination of incessant advances in sequencing technology producing large amounts of data and innovative bioinformatics approaches, designed to cope with this data flood, has led to new interesting results in the life sciences. Given the magnitude of sequence data to be processed, many bioinformatics tools rely on efficient solutions to a variety of complex string problems. These solutions include fast heuristic algorithms and advanced data structures, generally referred to as index structures. Although the importance of index structures is generally known to the bioinformatics community, the design and potency of these data structures, as well as their properties and limitations, are less understood. Moreover, the last decade has seen a boom in the number of variant index structures featuring complex and diverse memory-time trade-offs. This article brings a comprehensive state-of-the-art overview of the most popular index structures and their recently developed variants. Their features, interrelationships, the trade-offs they impose, but also their practical limitations, are explained and compared

Pattern matching of compressed terms and contexts and polynomial rewriting

A generalization of the compressed string pattern match that applies to terms with variables is investigated: Given terms s and t compressed by singleton tree grammars, the task is to find an instance of s that occurs as a subterm in t. We show that this problem is in NP and that the task can be performed in time O(ncjVar(s)j), including the construction of the compressed substitution, and a representation of all occurrences. We show that the special case where s is uncompressed can be performed in polynomial time. As a nice application we show that for an equational deduction of t to t0 by an equality axiom l = r (a rewrite) a single step can be performed in polynomial time in the size of compression of t and l; r if the number of variables is fixed in l. We also show that n rewriting steps can be performed in polynomial time, if the equational axioms are compressed and assumed to be constant for the rewriting sequence. Another potential application are querying mechanisms on compressed XML-data bases

Expert System for Crop Disease based on Graph Pattern Matching: A proposal

Para la agroindustria, las enfermedades en cultivos constituyen uno de los problemas más frecuentes que generan grandes pérdidas económicas y baja calidad en la producción. Por otro lado, desde las ciencias de la computación, han surgido diferentes herramientas cuya finalidad es mejorar la prevención y el tratamiento de estas enfermedades. En este sentido, investigaciones recientes proponen el desarrollo de sistemas expertos para resolver este problema haciendo uso de técnicas de minería de datos e inteligencia artificial, como inferencia basada en reglas, árboles de decisión, redes bayesianas, entre otras. Además, los grafos pueden ser usados para el almacenamiento de los diferentes tipos de variables que se encuentran presentes en un ambiente de cultivos, permitiendo la aplicación de técnicas de minería de datos en grafos, como el emparejamiento de patrones en los mismos. En este artículo presentamos una visión general de las temáticas mencionadas y una propuesta de un sistema experto para enfermedades en cultivos, basado en emparejamiento de patrones en grafos.For agroindustry, crop diseases constitute one of the most common problems that generate large economic losses and low production quality. On the other hand, from computer science, several tools have emerged in order to improve the prevention and treatment of these diseases. In this sense, recent research proposes the development of expert systems to solve this problem, making use of data mining and artificial intelligence techniques like rule-based inference, decision trees, Bayesian network, among others. Furthermore, graphs can be used for storage of different types of variables that are present in an environment of crops, allowing the application of graph data mining techniques like graph pattern matching. Therefore, in this paper we present an overview of the above issues and a proposal of an expert system for crop disease based on graph pattern matching