Speeding up transposition-invariant string matching

Finding the longest common subsequence (LCS) of two given sequences A=a₀a₁…am−1 and B=b₀b₁…bn−1 is an important and well studied problem. We consider its generalization, transposition-invariant LCS (LCTS), which has recently arisen in the field of music information retrieval. In LCTS, we look for the LCS between the sequences A+t=(a₀+t)(a₁+t)…(am−1+t) and B where t is any integer. We introduce a family of algorithms (motivated by the Hunt-Szymanski scheme for LCS), improving the currently best known complexity from O(mnloglogσ) to O(Dloglogσ+mn), where σ is the alphabet size and D?mn is the total number of dominant matches for all transpositions. Then, we demonstrate experimentally that some of our algorithms outperform the best ones from literature.     

A fast algorithm for computing a longest common increasing subsequence

Let A=〈a₁,a₂,…,am〉 and B=〈b₁,b₂,…,bn〉 be two sequences, where each pair of elements in the sequences is comparable. A common increasing subsequence of A and B is a subsequence 〈ai₁=bj₁,ai₂=bj₂,…,ail=bjl〉, where i₁<i₂<?<il and j₁<j₂<?<jl, such that for all 1?k<l, we have aik<aik+1. A longest common increasing subsequence of A and B is a common increasing subsequence of the maximum length. This paper presents an algorithm for delivering a longest common increasing subsequence in O(mn) time and O(mn) space.     

Classes of cost functions for string edit distance

Finding a sequence of edit operations that transforms one string of symbols into another with the minimum cost is a well-known problem. The minimum cost, or edit distance, is a widely used measure of the similarity of two strings. An important parameter of this problem is the cost function, which specifies the cost of each insertion, deletion, and substitution. We show that cost functions having the same ratio of the sum of the insertion and deletion costs divided by the substitution cost yield the same minimum cost sequences of edit operations. This leads to a partitioning of the universe of cost functions into equivalence classes. Also, we show the relationship between a particular set of cost functions and the longest common subsequence of the input strings. This work was supported in part by the U.S. Department of Defense and the U.S. Department of Energy.     

Variants of constrained longest common subsequence

We consider a variant of the classical Longest Common Subsequence problem called Doubly-Constrained Longest Common Subsequence (DC-LCS). Given two strings s₁ and s₂ over an alphabet Σ, a set Cs of strings, and a function Co:Σ→N, the DC-LCS problem consists of finding the longest subsequence s of s₁ and s₂ such that s is a supersequence of all the strings in Cs and such that the number of occurrences in s of each symbol σ∈Σ is upper bounded by Co(σ). The DC-LCS problem provides a clear mathematical formulation of a sequence comparison problem in Computational Biology and generalizes two other constrained variants of the LCS problem that have been introduced previously in the literature: the Constrained LCS and the Repetition-Free LCS. We present two results for the DC-LCS problem. First, we illustrate a fixed-parameter algorithm where the parameter is the length of the solution which is also applicable to the more specialized problems. Second, we prove a parameterized hardness result for the Constrained LCS problem when the parameter is the number of the constraint strings (|Cs|) and the size of the alphabet Σ. This hardness result also implies the parameterized hardness of the DC-LCS problem (with the same parameters) and its NP-hardness when the size of the alphabet is constant.     

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.     

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.     

一种XML文档结构相似度计算方法

对XML文档树路径模型进行扩展,加入了路径的频率信息.基于此路径-频率模型,提出一种带有位置仅重的基于路径的结构相似度计算方法(WLCS),并在此基础上提出基于路径频率的XML文档结构向量化方法.在真实数据集上的实验结果表明,WLCS方法召回率和准确率均高于当前存在的基于路径计算相似度的方法,适合于对来自不同DTD的XML文档的相似度比较.     

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.     

An almost-linear time and linear space algorithm for the longest common subsequence problem

There are two general approaches to the longest common subsequence problem. The dynamic programming approach takes quadratic time but linear space, while the nondynamic-programming approach takes less time but more space. We propose a new implementation of the latter approach which seems to get the best for both time and space for the DNA application.     

Most discriminating segment – Longest common subsequence (MDSLCS) algorithm for dynamic hand gesture classification

In this work, we consider the recognition of dynamic gestures based on representative sub-segments of a gesture, which are denoted as most discriminating segments (MDSs). The automatic extraction and recognition of such small representative segments, rather than extracting and recognizing the full gestures themselves, allows for a more discriminative classifier. A MDS is a sub-segment of a gesture that is most dissimilar to all other gesture sub-segments. Gestures are classified using a MDSLCS algorithm, which recognizes the MDSs using a modified longest common subsequence (LCS) measure. The extraction of MDSs from a data stream uses adaptive window parameters, which are driven by the successive results of multiple calls to the LCS classifier. In a preprocessing stage, gestures that have large motion variations are replaced by several forms of lesser variation. We learn these forms by adaptive clustering of a training set of gestures, where we reemploy the LCS to determine similarity between gesture trajectories. The MDSLCS classifier achieved a gesture recognition rate of 92.6% when tested using a set of pre-cut free hand digit (0–9) gestures, while hidden Markov models (HMMs) achieved an accuracy of 89.5%. When the MDSLCS was tested against a set of streamed digit gestures, an accuracy of 89.6% was obtained. At present the HMMs method is considered the state-of-the-art method for classifying motion trajectories. The MDSLCS algorithm had a higher accuracy rate for pre-cut gestures, and is also more suitable for streamed gestures. MDSLCS provides a significant advantage over HMMs by not requiring data re-sampling during run-time and performing well with small training sets.     

一种基于图的近重复视频子序列匹配算法

为了解决近重复视频检测中的效果和效率问题, 提出了一种基于图的近重复视频子序列匹配算法。将基于关键帧特征的相似性查询结果构建成匹配结果图, 进而将近重复视频检测转换成一个在匹配结果图中查找最长路径的问题。该算法有三个主要优势：a）它能在众多杂乱的匹配结果中找到最佳的匹配序列, 有效剔除了某些假“高相似度”匹配带来的噪声, 因而能在一定程度上弥补底层特征描述力的不足; b）由于它充分考虑和利用了视频序列的时序特性, 具有很高的近重复视频定位准确度; c）它能自动检测出匹配结果图中存在的多条离散路径, 从而能一次性检测出两段视频中可能存在多段近重复视频的情形。提出的算法不仅提高了检测的准确度, 而且提高了检测效率, 取得了良好的实践效果。     

A dynamic programming solution to a generalized LCS problem

In this paper, we consider a generalized longest common subsequence problem, the string-excluding constrained LCS problem. For the two input sequences X and Y of lengths n and m, and a constraint string P of length r, the problem is to find a common subsequence Z of X and Y excluding P as a substring and the length of Z is maximized. The problem and its solution were first proposed by Chen and Chao (2011) [1], but we found that their algorithm cannot solve the problem correctly. A new dynamic programming solution for the STR-EC-LCS problem is then presented in this paper. The correctness of the new algorithm is proved. The time complexity of the new algorithm is $O(nmr)$.     

Doubly-Constrained LCS and Hybrid-Constrained LCS problems revisited

We revisit two recently studied variants of the classic Longest Common Subsequence (LCS) problem, namely, the Doubly-Constrained LCS (DC-LCS) and Hybrid-Constrained LCS (HC-LCS) problems. We present finite automata based algorithms for both problems.     

Performance analysis of some simple heuristics for computing longest common subsequences

Although theLongest Common Subsequence (LCS)Problem has been studied by many researchers for years, heuristic methods have not been investigated before. In this paper we present a simple heuristic which guarantees to return a common subsequence of length at least 1/s that of the longest wheres is the number of different symbols in the input strings. Furthermore, we generalize the idea to several classes of heuristic algorithms. Surprisingly, we find that no other heuristic in these classes outperforms this simple algorithm. In other words, we show that any heuristic which uses only global information, such as number of symbol occurrences, might return a common subsequence as short as 1/s of the length of the longest. Analysis of the average performance of the simple heuristic fors=2 is also presented.This research was supported in part by ONR Grant N00014-87-K-0833.     

On the parameterized complexity of the fixed alphabet shortest common supersequence and longest common subsequence problems

We show that the fixed alphabet shortest common supersequence (SCS) and the fixed alphabet longest common subsequence (LCS) problems parameterized in the number of strings are W[1]-hard. Unless W[1]=FPT, this rules out the existence of algorithms with time complexity of O(f(k)nα) for those problems. Here n is the size of the problem instance, α is constant, k is the number of strings and f is any function of k. The fixed alphabet version of the LCS problem is of particular interest considering the importance of sequence comparison (e.g. multiple sequence alignment) in the fixed length alphabet world of DNA and protein sequences.     

A new relevance feedback technique for iconic image retrieval based on spatial relationships

Due to the popularity of Internet and the growing demand of image access, the volume of image databases is exploding. Hence, we need a more efficient and effective image searching technology. Relevance feedback technique has been popularly used with content-based image retrieval (CBIR) to improve the precision performance, however, it has never been used with the retrieval systems based on spatial relationships. Hence, we propose a new relevance feedback framework to deal with spatial relationships represented by a specific data structure, called the 2D B_e-string. The notions of relevance estimation and query reformulation are embodied in our method to exploit the relevance knowledge. The irrelevance information is collected in an irrelevant set to rule out undesired pictures and to expedite the convergence speed of relevance feedback. Our system not only handles picture-based relevance feedback, but also deals with region-based feedback mechanism, such that the efficacy and effectiveness of our retrieval system are both satisfactory.     

Applying VSM and LCS to develop an integrated text retrieval mechanism

Text retrieval has received a lot of attention in computer science. In the text retrieval field, the most widely-adopted similarity technique is using vector space models (VSM) to evaluate the weight of terms and using Cosine, Jaccard or Dice to measure the similarity between the query and the texts. However, these similarity techniques do not consider the effect of the sequence of the information. In this paper, we propose an integrated text retrieval (ITR) mechanism that takes the advantage of both VSM and longest common subsequence (LCS) algorithm. The key idea of the ITR mechanism is to use LCS to re-evaluate the weight of terms, so that the sequence and weight relationships between the query and the texts can be considered simultaneously. The results of mathematical analysis show that the ITR mechanism can increase the similarity on Jaccard and Dice similarity measurements when a sequential relationship exists between the query and the texts.     

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.