For any m strings of total length n, we propose an O(mn log n)-time, O(n)-space algorithm that finds a maximal common subsequence of all the strings, in the sense that inserting any character in it no longer yields a common subsequence of them. Such a common subsequence could be treated as indicating a nontrivial common structure we could find in the strings since it is NP-hard to find any longest common subsequence of the strings.

A lot of work has been conducted on time series classification and similarity search over the past decades. However, the classification of a time series with high accuracy is still insufficient in applications such as ubiquitous or sensor systems. In this paper, a novel textual approximation of a time series, called TAX, is proposed to achieve high accuracy time series classification. l-TAX, an extended version of TAX that shows promising classification accuracy over TAX and other existing methods, is also proposed. We also provide a comprehensive comparison between TAX and l-TAX, and discuss the benefits of both methods. Both TAX and l-TAX transform a time series into a textual structure using existing document retrieval methods and bioinformatics algorithms. In TAX, a time series is represented as a document like structure, whereas l-TAX used a sequence of textual symbols. This paper provides a comprehensive overview of the textual approximation and techniques used by TAX and l-TAX

The style of a gesture provides significant information for communication, and thus understanding the style is of great importance in improving gestural interfaces using hand gestures. We present a novel method to estimate temporal and spatial scale—which are considered principal elements of the style—of hand gestures. Gesture synchronization is proposed for matching progression between spatio-temporally varying gestures, and scales are estimated based on the progression matching. For comparing gestures of various sizes and speeds, gesture representation is defined by adopting turning angle representation. Also, LCSS is used as a similarity measure for reliability and robustness to noise and outliers. Performance of our algorithm is evaluated with synthesized data to show the accuracy and robustness to noise and experiments are carried out using recorded hand gestures to analyze applicability under real-world situations.

This article presents an algorithm that solves an on-line version of the longest common subsequence (LCS) problem for two strings over a constant alphabet in O(d+n) time and O(m+d) space, where m is the length of the shorter string, the whole of which is given to the algorithm in advance, n is the length of the longer string, which is given as a data stream, and d is the number of dominant matches between the two strings. A new upper bound, O(p(m-q)), of d is also presented, where p is the length of the LCS of the two strings, and q is the length of the LCS of the shorter string and the m-length prefix of the longer string.

The optimal alignment of two given biosequences is mathematically optimal, but it may not be a biologically optimal one. To investigate more possible alignments with biological meaning, one can relax the scoring functions to get near-optimal alignments. Though the near optimal alignments increase the possibility of finding the correct alignment, they may confuse the biologists because the size of candidates is large. In this paper, we present the filter scheme for the near-optimal alignments. An easy method for tracing the near-optimal alignments and an algorithm for filtering those alignments are proposed. The time complexity of our algorithm is O(dmn) in the worst case, where d is the maximum distance between the near-optimal alignments and the optimal alignment, and m and n are the lengths of the input sequences, respectively.

Several two-dimensional largest common subpatterns (LCP) between pictures are defined and their computing methods are proposed. The time and space complexities of the computing methods are O(IJMN) to obtain the size of LCPs between a picture with IJ pixels and a picture with MN pixels. These LCPs can be used as similarity measures between pictures and can be applied to texture recognition and classification.