The edit distance between strings A and B is defined as the minimum number of edit operations needed in converting A into B or vice versa. The Levenshtein edit distance allows three types of operations: an insertion, a deletion or a substitution of a character. The Damerau edit distance allows the previous three plus in addition a transposition between two adjacent characters. To our best knowledge the best current practical algorithms for computing these edit distances run in time O(dm) and O(⌈m/w⌉(n + σ)), where d is the edit distance between the two strings, m and n are their lengths (m ≤ n), w is the computer word size and σ is the size of the alphabet. In this paper we present an algorithm that runs in time O(⌈d/w⌉m + ⌈n/w⌉σ) or O(⌈d/w⌉n + ⌈m/w⌉σ). The structure of the algorithm is such, that in practice it is mostly suitable for testing whether the edit distance between two strings is within some pre-determined error threshold. We also present some initial test results with thresholded edit distance computation. In them our algorithm works faster than the original algorithm of Myers.

A Bit-Vector Algorithm for Computing Levenshtein and Damerau Edit Distances.

The edit distance is the measure that quantifies the difference between two strings. It is an important concept because it has its usage in many domains such as natural language processing, spell checking, genome matching, and pattern recognition. Edit distance is also known as Levenshtein distance. Sequentially, the edit distance is computed by using dynamic programming based strategy that may not provide results in reasonable time when input strings are large. In this work, a distributed algorithm is presented for parallel edit distance computation. The proposed algorithm is both time and space efficient. It is evaluated on a hybrid setup of distributed and shared memory systems. Results suggest that the proposed algorithm achieves significant performance gain over the existing parallel approach.

Distributed Algorithm for Parallel Edit Distance Computation

Today, as we expect the appearance of the first supercomputer with exascale capabilities, some tough questions remain to be solved. A main challenge of the upcoming exascale era will appear around the ability to process extremely large datasets of several petaand exabytes effectively and efficiently. This needs to be addressed with new management and architectural approaches, focusing on modular, integrated and light-weight solutions, which enable end-users across all scientific domains to utilize these future supercomputing systems. This special issue gives an overview on approaches focusing of these challenges and exacting applications, requiring exascale-ready compute and data services. In their paper Bobák et al. [2] present an exascale reference architecture as a layered framework to overcome exascale challenges, developed within the PROCESS project. Their modular and service-oriented approach enables low-overhead

Preface to the Special Issue on Providing Computing Solutions for Exascale Challenges

Sequence alignment remains a fundamental problem with practical applications ranging from pattern recognition to computational biology. Traditional algorithms based on dynamic programming are hard to parallelize, require significant amounts of memory, and fail to scale for large inputs. This work presents eWFA-GPU, a GPU (graphics processing unit)-accelerated tool to compute the exact edit-distance sequence alignment based on the wavefront alignment algorithm (WFA). This approach exploits the similarities between the input sequences to accelerate the alignment process while requiring less memory than other algorithms. Our implementation takes full advantage of the massive parallel capabilities of modern GPUs to accelerate the alignment process. In addition, we propose a succinct representation of the alignment data that successfully reduces the overall amount of memory required, allowing the exploitation of the fast shared memory of a GPU. Our results show that our GPU implementation outperforms by 3-9× the baseline edit-distance WFA implementation running on a 20 core machine. As a result, eWFA-GPU is up to 265 times faster than state-of-the-art CPU implementation, and up to 56 times faster than state-of-the-art GPU implementations.

Accelerating Edit-Distance Sequence Alignment on GPU using the Wavefront Algorithm

Sequence alignment remains a fundamental problem with practical applications ranging from pattern recognition to computational biology. Traditional algorithms based on dynamic programming are hard to parallelize, require significant amounts of memory, and fail to scale for large inputs. This work presents eWFA-GPU, a GPU (graphics processing unit)-accelerated tool to compute the exact edit-distance sequence alignment based on the wavefront alignment algorithm (WFA). This approach exploits the similarities between the input sequences to accelerate the alignment process while requiring less memory than other algorithms. Our implementation takes full advantage of the massive parallel capabilities of modern GPUs to accelerate the alignment process. In addition, we propose a succinct representation of the alignment data that successfully reduces the overall amount of memory required, allowing the exploitation of the fast shared memory of a GPU. Our results show that our GPU implementation outperforms by 3-9&#x00D7; the baseline edit-distance WFA implementation running on a 20 core machine. As a result, eWFA-GPU is up to 265 times faster than state-of-the-art CPU implementation, and up to 56 times faster than state-of-the-art GPU implementations. 

/pdf/accelerating-edit-distance-sequence-alignment-on-gpu-using-2zrdntgj.pdf

Accelerating Edit-Distance Sequence Alignment on GPU Using the Wavefront Algorithm

Edit distance has applications in many domains such as bioinformatics, spell checking, plagiarism checking, query optimization, speech recognition, and data mining. Traditionally, edit distance is computed by dynamic programming based sequential solution which becomes infeasible for large problems. In this paper, we introduce NvPD, a novel algorithm for parallel edit distance computation by resolving dependencies in the conventional dynamic programming based solution. We also establish the correctness of modified dependencies. NvPD exhibits certain characteristics such as balanced workload among processors, less synchronization overhead, maximum utilization of resources and it can exploit spatial locality. It requires $$\min (m,n)$$
 steps to complete as compared to diagonal based approach that completes in $$\max (m,n)$$
 . Experimental evaluation using variety of random and real life data sets over shared memory multi-core systems and graphic processing units (GPUs) show that NvPD outperforms state-of-the-art parallel edit distance algorithms.

NvPD: novel parallel edit distance algorithm, correctness, and performance evaluation

/pdf/a-novel-parallel-algorithm-for-edit-distance-computation-460isir9ry.pdf

A Novel Parallel Algorithm for Edit Distance Computation

Space-efficient computation of parallel approximate string matching

Edit distance is the most widely used method to quantify similarity between two strings. We investigate the problem of similarity search under edit distance. Given a collection of sequences, the goal of similarity search under edit distance is to find sequences in the collection that are similar to a given query sequence where the similarity score is computed using edit distance. The canonical method of computing edit distance between two strings uses a dynamic programming-based approach that runs in quadratic time and space, which may not provide results in a reasonable amount of time for large sequences. It advocates for parallel algorithms to reduce the time taken by edit distance computation. To this end, we present scalable parallel algorithms to support efficient similarity search under edit distance. The efficiency and scalability of the proposed algorithms is demonstrated through an extensive set of experiments on real datasets. Moreover, to address the problem of uneven workload across different processing units, which is mainly caused due to the significant variance in the size of the sequences, different data distribution schemes are discussed and empirically analyzed. Experimental results have shown that the speedup achieved by the hybrid approach over inter-task and intra-task parallelism is 18 and 13, respectively.

/pdf/toward-efficient-similarity-search-under-edit-distance-on-1pqeblu8.pdf

Muhammad Umair Sadiq

Papers

NvPD: novel parallel edit distance algorithm, correctness, and performance evaluation

Distributed Algorithm for Parallel Edit Distance Computation

A Novel Parallel Algorithm for Edit Distance Computation

Space-efficient computation of parallel approximate string matching

Toward Efficient Similarity Search under Edit Distance on Hybrid Architectures