A Grammar Compression Algorithm based on Induced Suffix Sorting

We introduce GCIS, a grammar compression algorithm based on the induced suffix sorting algorithm SAIS, introduced by Nong et al. in 2009. Our solution builds on the factorization performed by SAIS during suffix sorting. We construct a context-free grammar on the input string which can be further reduced into a shorter string by substituting each substring by its correspondent factor. The resulting grammar is encoded by exploring some redundancies, such as common prefixes between suffix rules, which are sorted according to SAIS framework. When compared to well-known compression tools such as Re-Pair and 7-zip, our algorithm is competitive and very effective at handling repetitive string regarding compression ratio, compression and decompression running time

An Elegant Algorithm for the Construction of Suffix Arrays

The suffix array is a data structure that finds numerous applications in string processing problems for both linguistic texts and biological data. It has been introduced as a memory efficient alternative for suffix trees. The suffix array consists of the sorted suffixes of a string. There are several linear time suffix array construction algorithms (SACAs) known in the literature. However, one of the fastest algorithms in practice has a worst case run time of $O(n^2)$. The problem of designing practically and theoretically efficient techniques remains open. In this paper we present an elegant algorithm for suffix array construction which takes linear time with high probability; the probability is on the space of all possible inputs. Our algorithm is one of the simplest of the known SACAs and it opens up a new dimension of suffix array construction that has not been explored until now. Our algorithm is easily parallelizable. We offer parallel implementations on various parallel models of computing. We prove a lemma on the $\ell$-mers of a random string which might find independent applications. We also present another algorithm that utilizes the above algorithm. This algorithm is called RadixSA and has a worst case run time of $O(n\log{n})$. RadixSA introduces an idea that may find independent applications as a speedup technique for other SACAs. An empirical comparison of RadixSA with other algorithms on various datasets reveals that our algorithm is one of the fastest algorithms to date. The C++ source code is freely available at http://www.engr.uconn.edu/~man09004/radixSA.zi

On An Improved Parallel Construction Of Suffix Arrays For Low Bandwidth Pc-Cluster.

An algorithm for the parallel construction of suffix arrays generation for any texts with larger alphabet size on distributed memory architecture is presente

Inducing Suffix and LCP Arrays in External Memory

We consider full text index construction in external memory (EM). Our first contribution is an inducing algorithm for suffix arrays in external memory, which utilizes an efficient EM priority queue and runs in sorting complexity. Practical tests show that this algorithm outperforms the previous best EM suffix sorter [Dementiev et al., JEA 2008] by a factor of about two in time and I/O-volume. Our second contribution is to augment the first algorithm to also construct the array of longest common prefixes (LCPs). This yields the first EM construction algorithm for LCP arrays. The overhead in time and I/O volume for this extended algorithm over plain suffix array construction is roughly two. Our algorithms scale far beyond problem sizes previously considered in the literature (text size of 80 GiB using only 4 GiB of RAM in our experiments).

High-Performance Meta-Genomic Gene Identification

Computational Genomics, or Computational Genetics, refers to the use of computational and statistical analysis for understanding the structure and the function of genetic material in organisms. The primary focus of research in computational genomics in the past three decades has been the understanding of genomes and their functional elements by analyzing biological sequence data. The high demand for low-cost sequencing has driven the development of highthroughput sequencing technologies, next-generation sequencing (NGS), that parallelize the sequencing process, producing thousands or millions of sequences concurrently. Moore’s Law is the observation that the number of transistors on integrated circuits doubles approximately every two years; correspondingly, the cost per transistor halves. The cost of DNA sequencing declines much faster, which implies more new DNA data will be obtained. This large-scale sequence data, produced with high throughput sequencing technologies, needs to be processed in a time-effective and cost-effective manner. In this dissertation, we present a high-performance meta-genome gene identification framework. This framework includes four modules: filter, alignment, error correction, and gene identification. The following chapters describe the proposed design and evaluation of this pipeline. The most computationally expensive kernel in the framework is the alignment procedure. Thus, the filter module is developed to determine unnecessary alignment operations. Without the filter module, the alignment module requires 1.9 hours to complete all-to-all alignment on a test file of size 512,000 sequences with each sequence average length 750 base pairs by using ten Kepler K20 NVIDIA GPU. On the other hand, when combined with the filter kernel, the total time is 11.3 minutes. Note that the ideal speedup is nearly 91.4 times faster when new alignment kernel is run on ten GPUs ( 10*9.14). We conclude that accuracy can be achieved at the expense of more resources while operating frequency can still be maintained

Fast parallel skew and prefix‐doubling suffix array construction on the GPU

Suffix arrays are fundamental full-text index data structures of importance to a broad spectrum of applications in such fields as bioinformatics, Burrows-Wheeler Transform (BWT)-based lossless data compression, and information retrieval. In this work, we propose and implement two massively parallel approaches on the GPU based on two classes of suffix array construction algorithms. The first, parallel skew, makes algorithmic improvements to the previous work of Deo and Keely to achieve a speedup of 1.45x over their work. The second, a hybrid skew and prefix-doubling implementation, is the first of its kind on the GPU and achieves a speedup of 2.3–4.4x over Osipov’s prefix-doubling and 2.4–7.9x over our skew implementation on large datasets. Our implementations rely on two efficient parallel primitives, a merge and a segmented sort. We theoretically analyze the two formulations of suffix array construction algorithms and show performance comparisons on a large variety of practical inputs. We conclude that, with the novel use of our efficient segmented sort, prefix-doubling is more competitive than skew on the GPU. We also demonstrate the effectiveness of our methods in our implementations of the Burrows-Wheeler transform and in a parallel FM-index for pattern searching. This is the submitted version of the paper

Algorithm Engineering for fundamental Sorting and Graph Problems

Fundamental Algorithms build a basis knowledge for every computer science undergraduate or a professional programmer. It is a set of basic techniques one can find in any (good) coursebook on algorithms and data structures. In this thesis we try to close the gap between theoretically worst-case optimal classical algorithms and the real-world circumstances one face under the assumptions imposed by the data size, limited main memory or available parallelism