相关论文: Computing the Number of Longest Common Subsequence…
We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…
This paper studies the large-scale subspace clustering (LSSC) problem with million data points. Many popular subspace clustering methods cannot directly handle the LSSC problem although they have been considered as state-of-the-art methods…
Long Short-Term Memory (LSTM) Networks and Convolutional Neural Networks (CNN) have become very common and are used in many fields as they were effective in solving many problems where the general neural networks were inefficient. They were…
Encoding time-series with Linear Dynamical Systems (LDSs) leads to rich models with applications ranging from dynamical texture recognition to video segmentation to name a few. In this paper, we propose to represent LDSs with…
Matching pursuit algorithms are an important class of algorithms in signal processing and machine learning. We present a blended matching pursuit algorithm, combining coordinate descent-like steps with stronger gradient descent steps, for…
The {\em shortest common superstring} and the {\em shortest common supersequence} are two well studied problems having a wide range of applications. In this paper we consider both problems with resource constraints, denoted as the…
The notion of the cover is a generalization of a period of a string, and there are linear time algorithms for finding the shortest cover. The seed is a more complicated generalization of periodicity, it is a cover of a superstring of a…
Given a sequence of integers, we want to find a longest increasing subsequence of the sequence. It is known that this problem can be solved in $O(n \log n)$ time and space. Our goal in this paper is to reduce the space consumption while…
This paper presents convergence acceleration, a method for computing efficiently the limit of numerical sequences as a typical application of streams and higher-order functions.
We present a simple algorithm for computing the document array given a string collection and its suffix array as input. Our algorithm runs in linear time using constant additional space for strings from constant alphabets.
Let us call a sequence of numbers heapable if they can be sequentially inserted to form a binary tree with the heap property, where each insertion subsequent to the first occurs at a leaf of the tree, i.e. below a previously placed number.…
The Longest Common Increasing Subsequence (LCIS) is a variant of the classical Longest Common Subsequence (LCS), in which we additionally require the common subsequence to be strictly increasing. While the well-known "Four Russians"…
A method for encoding and decoding spectrum shaped binary run-length constrained sequences is described. The binary sequences with predefined range of exponential sums are introduced. On the base of Cover's enumerative scheme, recurrence…
Two general methods for establishing the logarithmic behavior of recursively defined sequences of real numbers are presented. One is the interlacing method, and the other one is based on calculus. Both methods are used to prove logarithmic…
The equidistant subsequence pattern matching problem is considered. Given a pattern string $P$ and a text string $T$, we say that $P$ is an \emph{equidistant subsequence} of $T$ if $P$ is a subsequence of the text such that consecutive…
We find a formula for the number of solutions of linear congruence systems, by using elementary methods.
We present an algorithm computing the longest periodic subsequence of a string of length $n$ in $O(n^7)$ time with $O(n^4)$ words of space. We obtain improvements when restricting the exponents or extending the search allowing the reported…
New algorithms are devised for finding the maxima of multidimensional point samples, one of the very first problems studied in computational geometry. The algorithms are very simple and easily coded and modified for practical needs. The…
The longest common prefix array is a very advantageous data structure that, combined with the suffix array and the Burrows-Wheeler transform, allows to efficiently compute some combinatorial properties of a string useful in several…
This paper addresses the Longest Filled Common Subsequence (LFCS) problem, a challenging NP-hard problem with applications in bioinformatics, including gene mutation prediction and genomic data reconstruction. Existing approaches, including…