Using string matching to detect video transitions

The detection of shot boundaries in videos captures the structure of the image sequences by the identification of transitional effects. This task is important in the video indexing and retrieval domain. The video slice or visual rhythm is a single two-dimensional image sampling that has been used to detect several types of video events, including transitions. We use the longest common subsequence (LCS) between two strings to transform the video slice into one-dimensional signals obtaining a highly simplified representation of the video content. We also developed a chain of mathematical morphology operations over these signals leading to the detection of the most frequent video transitions, namely, cut, fade, and wipe. The algorithms are tested with success with various genres of videos.     

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.     

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.     

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.     

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.     

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.     

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.     

Parallel comparison of run-length-encoded strings on a linear systolic array

The length of the longest common subsequence (LCS) between two strings of M and N characters can be computed by an O(M × N) dynamic programming algorithm, that can be executed in O(M + N) steps by a linear systolic array. It has been recently shown that the LCS between run-length-encoded (RLE) strings of m and n runs can be computed by an O(nM + Nm − nm) algorithm that could be executed in O(m + n) steps by a parallel hardware. However, the algorithm cannot be directly mapped on a linear systolic array because of its irregular structure.In this paper, we propose a modified algorithm that exhibits a more regular structure at the cost of a marginal reduction of the efficiency of RLE. We outline the algorithm and we discuss its mapping on a linear systolic array.     

Longest common subsequence between run-length-encoded strings: a new algorithm with improved parallelism

Data compression can be used to simultaneously reduce memory, communication and computation requirements of string comparison. In this paper we address the problem of computing the length of the longest common subsequence (LCS) between run-length-encoded (RLE) strings. We exploit RLE both to reduce the complexity of LCS computation from O(M×N) to O(mN+Mn−mn), where M and N are the lengths of the original strings and m and n the number of runs in their RLE representation, and to improve the inherent parallelism of the proposed algorithm, so that it may execute in O(m+n) steps on a systolic array of M+N units.We also discuss the application of the proposed algorithm to the related problem of edit distance (ED) computation.     

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 improved algorithm for the longest common subsequence problem

The Longest Common Subsequence problem seeks a longest subsequence of every member of a given set of strings. It has applications, among others, in data compression, FPGA circuit minimization, and bioinformatics. The problem is NP-hard for more than two input strings, and the existing exact solutions are impractical for large input sizes. Therefore, several approximation and (meta) heuristic algorithms have been proposed which aim at finding good, but not necessarily optimal, solutions to the problem. In this paper, we propose a new algorithm based on the constructive beam search method. We have devised a novel heuristic, inspired by the probability theory, intended for domains where the input strings are assumed to be independent. Special data structures and dynamic programming methods are developed to reduce the time complexity of the algorithm. The proposed algorithm is compared with the state-of-the-art over several standard benchmarks including random and real biological sequences. Extensive experimental results show that the proposed algorithm outperforms the state-of-the-art by giving higher quality solutions with less computation time for most of the experimental cases.     

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.     

Shift-or string matching with super-alphabets

Given a text T[1…n] and a pattern P[1…m] over some alphabet Σ of size σ, we want to find all the (exact) occurrences of P in T. The well-known shift-or algorithm solves this problem in time O(n⌈m/w⌉), where w is the number of bits in machine word, using bit-parallelism. We show how to extend the bit-parallelism in another direction, using super-alphabets. This gives a speed-up by a factor s, where s is the number of characters processed simultaneously. The algorithm is implemented, and we show that it works well in practice too. The result is the fastest known algorithm for exact string matching for short patterns and small alphabets.     

Efficient parameterized string matching

In parameterized string matching the pattern P matches a substring t of the text T if there exist a bijective mapping from the symbols of P to the symbols of t. We give simple and practical algorithms for finding all such pattern occurrences in sublinear time on average. The algorithms work for a single and multiple patterns.     

基于高效精确的最大公共子序列的视频片段匹配

为视频序列匹配提出一个高效精确的最大公共子序列（Efficient and Effective Longest Common Subsequence,EELCS）算法。首先,利用矢量量化（Vector Quantization,VQ）将多维最大公共子序列算法（Multi-dimensional LCS,MLCS）中元素对匹配过程中的实际距离的计算简化成比较操作,较原始的最大公共子序列匹配算法（Original LCS,OLCS）,该处理不仅可以继承MLCS的可应用到实际多维时序匹配问题中的优点,同时大大降低了匹配的复杂度;然后进一步区分待匹配序列中由于匹配子序列和未匹配子序列在时间轴上连续性而产生的差异;最后将该算法应用到视频片段的匹配中。实验结果表明,与具有代表性的基于时间规扭曲的最大公共子序列（Time-Warped LCS,T-WLCS）和连续最大公共子序列（Continuous LCS,CLCS）相比,该算法能较好地应用于视频序列的匹配。     

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.     

Improving practical exact string matching

We present improved variations of the BNDM algorithm for exact string matching. At each alignment our bit-parallel algorithms process a q-gram before testing the state variable. In addition we apply reading a 2-gram in one instruction. Our point of view is practical efficiency of algorithms. Our experiments show that the new variations are faster than earlier algorithms in many cases.