An Efficient Systolic Algorithm for the Longest Common Subsequence Problem

A longest common subsequence (LCS) of two strings is a common subsequence of the two strings of maximal length. The LCS problem is to find an LCS of two given strings and the length of the LCS (LLCS). In this paper, a fast linear systolic algorithm that improves on previous systolic algorithms for solving the LCS problem is presented. For two given strings of length m and n, where m n, the LLCS and an LCS can be found in m + 2n – 1 time steps. This algorithm achieves the tight lower bound of the time complexity under the situation where symbols are input sequentially to a linear array of n processors. The systolic algorithm can be modified to take only m + n steps on multicomputers by using the scatter operation.     

A New Efficient Algorithm for Computing the Longest Common Subsequence

The Longest Common Subsequence (LCS) problem is a classic and well-studied problem in computer science. The LCS problem is a common task in DNA sequence analysis with many applications to genetics and molecular biology. In this paper, we present a new and efficient algorithm for solving the LCS problem for two strings. Our algorithm runs in O(ℛlog log n+n) time, where ℛ is the total number of ordered pairs of positions at which the two strings match. Preliminary version appeared in [24]. C.S. Iliopoulos is supported by EPSRC and Royal Society grants. M.S. Rahman is supported by the Commonwealth Scholarship Commission in the UK under the Commonwealth Scholarship and Fellowship Plan (CSFP) and is on Leave from Department of CSE, BUET, Dhaka-1000, Bangladesh.     

最长公共子序列算法在填空题评分程序中的应用

讨论最长公共子序列算法在填空题评分中的应用,并具体设计一种基于网络环境下,考试系统中的填空题题型的通用答案识别逻辑,在独立学院网络考试系统中操作可行。     

Implementation of a Sliding Memory Plane Image Processor

This paper presents architectures and implementation of a Sliding Memory Plane (SliM) Image Processor to build a SIMD parallel computer. The paper also proposes an enhanced multiplication algorithm to reduce the gate count and the number of cycles. The SliM chip consists of mesh-connected 5×5 PEs. Due to the idea ofsliding, that is, overlapping the inter-PE communication time with the computation time, SliM can greatly reduce the inter-PE communication overhead. In addition, four operations corresponding to ALU, shift, data I/O, and inter-PE communication can be grouped into an instruction to be executed in a cycle simultaneously. The implemented SliM chip operates at 25 MHz and gives 625 MIPS. Because of a mesh topology, a large number of chips can be easily connected to form a SIMD parallel computer. We have implemented the scalable SliM Array Processor and developed parallel algorithms for real-time image processing.     

Analysis of Evolutionary Algorithms for the Longest Common Subsequence Problem

In the longest common subsequence problem the task is to find the longest sequence of letters that can be found as a subsequence in all members of a given finite set of sequences. The problem is one of the fundamental problems in computer science with the task of finding a given pattern in a text as an important special case. It has applications in bioinformatics; problem-specific algorithms and facts about its complexity are known. Motivated by reports about good performance of evolutionary algorithms for some instances of this problem a theoretical analysis of a generic evolutionary algorithm is performed. The general algorithmic framework encompasses EAs as different as steady state GAs with uniform crossover and randomized hill-climbers. For all these algorithms it is proved that even rather simple special cases of the longest common subsequence problem can neither be solved to optimality nor approximately be solved up to an approximation factor arbitrarily close to 2.     

APPLICATION-SPECIFIC ARRAY PROCESSORS FOR THE LONGEST COMMON SUBSEQUENCE PROBLEM OF THREE SEQUENCES ∗ †

Abstract

We design linear time systolic-based parallel algorithms that run on two-dimensional arrays for both computing the length and recovering a longest common subsequence of three given sequences that are appropriate for very large-scale integration (VLSI) implementation. These problems have been qualified to be difficult to be solved in linear time in [14], and our approach, which generalizes the methods used for determining a longest common subsequence of two strings [28,38] to the case of three strings, enables to solve both problems in linear time. Given the three sequences A, B and C of length n, m and l (n ≤ m ≤ l;), we provide an algorithm that computes the length p of their longest common subsequence on a modular I/O bounded one-way two-dimensional array of nm processors in n + 2m + l? 1 time-steps. To compute a longest common subsequence of the three given strings, we show that each processor of the above array requires an O(min{n,p\) local storage to solve the problem in In + 1m + 1 + p — 2 time-steps.     

基于多态并行处理器的生物计算并行实现

针对传统的生物计算中DNA序列保守序列的识别（模体识别）和最长公共子序列计算需要较大的数据量、计算量,以及功耗大等问题,文中提出了两种基于PAAG多态并行处理器的并行算法,该并行处理器能够支持数据、线程、指令多种并行。通过编程在PAAG多态并行处理的处理单元（ PE）上开发了相应的串行和并行程序,将计算的不同过程分派到不同的处理单元（ PE）上进行处理,实现了不同粒度算法的并行。实验结果表明,文中提出的并行算法使模体识别和最长公共子序列的计算效率得到明显提高。     

A Coarse-Grained Parallel Algorithm for the All-Substrings Longest Common Subsequence Problem

Given two strings A and B of lengths n_a and n_b, respectively, the All-substrings Longest Common Subsequence (ALCS) problem obtains, for any substring B' of B, the length of the longest string that is a subsequence of both A and B'. The sequential algorithm for this problem takes O(n_a n_b) time and O(n_b) space. We present a parallel algorithm for the ALCS problem on the Coarse-Grained Multicomputer (BSP/CGM) model with p < √n_a processors, that takes O(n_a n_b/p) time, O(log p) communication rounds and O(n_b √n_a) space per processor. The proposed algorithm also solves the basic Longest Common Subsequence (LCS) problem that finds the longest string (and not only its length) that is a subsequence of both A and B. To our knowledge, this is the best BSP/CGM algorithm in the literature for the LCS and ALCS problems.     

Design of Processor Arrays for Reconfigurable Architectures

This paper deals with the design of processor arrays for regular algorithms. The design is constrained by limited implementation cost characterizing a reconfigurable architecture. The objective of the design is to minimize the latency of the processor array. The presented approach to determine a scheduling function leading to the minimal latency of the processor array is formulated as a linear program that incorporates 1) the selection of modules to be implemented in processors to execute operations of the algorithm, 2) the binding of operations to modules, 3) the computation of the number of registers, 4) the limitation of implementation cost for modules and registers, 5) the determination of the size of partitions that allows to match the limited implementation cost.     

具有高效缓冲策略的运动估计阵列处理器结构

基于改进的线性处理器阵列,提出了一种用于全搜索运动估计的阵列处理器结构,它可以并行执行运算而只要求串行的数据输入.分析表明这种结构不仅执行效率高,而且内部缓冲区很小.由于其简单的结构和规则的数据流,它可以方便地在FPGA器件中实现,用作实时编码器的协处理器.     

A fast and practical bit-vector algorithm for the Longest Common Subsequence problem

This paper presents a new practical bit-vector algorithm for solving the well-known Longest Common Subsequence (LCS) problem. Given two strings of length m and n, nm, we present an algorithm which determines the length p of an LCS in O(nm/w) time and O(m/w) space, where w is the number of bits in a machine word. This algorithm can be thought of as column-wise “parallelization” of the classical dynamic programming approach. Our algorithm is very efficient in practice, where computing the length of an LCS of two strings can be done in linear time and constant (additional/working) space by assuming that mw.     

Beam search for the longest common subsequence problem

The longest common subsequence problem is a classical string problem that concerns finding the common part of a set of strings. It has several important applications, for example, pattern recognition or computational biology. Most research efforts up to now have focused on solving this problem optimally. In comparison, only few works exist dealing with heuristic approaches. In this work we present a deterministic beam search algorithm. The results show that our algorithm outperforms the current state-of-the-art approaches not only in solution quality but often also in computation time.     

New efficient algorithms for the LCS and constrained LCS problems

In this paper, we study the classic and well-studied longest common subsequence (LCS) problem and a recent variant of it, namely the constrained LCS (CLCS) problem. In the CLCS problem, the computed LCS must also be a supersequence of a third given string. In this paper, we first present an efficient algorithm for the traditional LCS problem that runs in O(Rloglogn+n) time, where R is the total number of ordered pairs of positions at which the two strings match and n is the length of the two given strings. Then, using this algorithm, we devise an algorithm for the CLCS problem having time complexity O(pRloglogn+n) in the worst case, where p is the length of the third string.     

Efficient Algorithms for the Block Hessenberg Form

We investigate in this paper the performance of parallel algorithms for computing the controllable part of a control linear system, with application to the computation of minimal realizations. Our approach is based on a method that transforms the matrices of the system to block Hessenberg form by using rank-revealing orthogonal factorizations.The experimental analysis on a high performance architecture includes two rank-revealing numerical tools: the SVD and the rank-revealing QR factorizations. Results are also reported, using the rank-revealing QR factorizations, on a parallel distributed architecture.     

A fast and simple algorithm for computing the longest common subsequence of run-length encoded strings

Let X and Y be two strings of lengths n and m, respectively, and k and l, respectively, be the numbers of runs in their corresponding run-length encoded forms. We propose a simple algorithm for computing the longest common subsequence of two given strings X and Y in O(kl+min{p₁,p₂}) time, where p₁ and p₂ denote the numbers of elements in the bottom and right boundaries of the matched blocks, respectively. It improves the previously known time bound O(min{nl,km}) and outperforms the time bounds O(kllogkl) or O((k+l+q)log(k+l+q)) for some cases, where q denotes the number of matched blocks.     

最小生成树的高效异步并行算法

在ＭＩＭＤ－ＳＭ并行计算模型上，本文给出了时间复杂性为Ｏ（ｎ（ｎ／ｐ＋ｌｏｇｐ））的最小生成树的异步并行算法，其中ｎ，ｐ（１≤ｐ≤ｎ）分别表示图的顶点数和处理机的个数。     

Combinatorial Algorithms for the Unsplittable Flow Problem

We provide combinatorial algorithms for the unsplittable flow problem (UFP) that either match or improve the previously best results. In the UFP we are given a (possibly directed) capacitated graph with n vertices and m edges, and a set of terminal pairs each with its own demand and profit. The objective is to connect a subset of the terminal pairs each by a single flow path subject to the capacity constraints such that the total profit of the connected pairs is maximized.We consider three variants of the problem. First is the classical UFP in which the maximum demand is at most the minimum edge capacity. It was previously known to have an O(√m) approximation algorithm; the algorithm is based on the randomized rounding technique and its analysis makes use of the Chernoff bound and the FKG inequality.We provide a combinatorial algorithm that achieves the same approximation ratio and whose analysis is considerably simpler. Second is the extended UFP in which some demands might be higher than edge capacities. Our algorithm for this case improves the best known approximation ratio. We also give a lower bound that shows that the extended UFP is provably harder than the classical UFP. Finally, we consider the bounded UFP in which the maximum demand is at most 1/K times the minimum edge capacity for some K > 1. Here we provide combinatorial algorithms that match the currently best known algorithms. All of our algorithms are strongly polynomial and some can even be used in the online setting.     

Scheduling Functions for Spatiotemporal Mapping of d-Dimensional Algorithms with Homogeneous Dependences on (d-2)-Dimensional Parallel Architectures

A formalized method is proposed for construction of scheduling functions for spatiotemporal mapping of d-dimensional algorithms represented by systems of homogeneous recurrence equations on (d-2)-dimensional parallel architectures. Basic operations of the algorithms are scheduled separately by means of functions with rational coefficients.     

The two list algorithm for the knapsack problem on a FPS T20

The advent of parallel machines brought about a controverse in the domain of parallel algorithms: is it worth to conceive parallel algorithms for NP-complete problems? In this work we present a parallel implementation of a sequential algorithm from Horowitz and Sahni for the knapsack problem on a FPS T20. Our aim is to establish some experimental results in order to allow comparisons for forthcoming works. The results show that the development of theory and technology yields the computation tractability of very large knapsack problems.     

An Efficient Communication Scheduling Method for the Processor Mapping Technique Applied Data Redistribution

Array redistribution is usually required for more efficiently executing a data-parallel program on distributed memory multi-computers. In performing array redistribution using synchronous communication mode, data communications among the processors should be properly arranged to avoid incurring higher data transfer cost. Some efficient communication scheduling methods for the Block-Cyclic redistribution have been proposed. On the other hand, the processor mapping technique can help reduce the data transfer cost of redistribution. To avoid degrading the benefit of data transfer cost reduction, it is needed to construct optimal communication schedules for the redistribution in which the processor mapping technique is applied. In this paper, we present a unified approach to constructing optimal communication schedules for the processor mapping technique applied Block-Cyclic redistribution. The proposed method is founded on the processor mapping technique and can more efficiently construct the required communication schedules than other optimal scheduling methods.