Alexander Tiskin

Alexander Tiskin
Saint Petersburg State University | SPBU

Doctor of Philosophy

About

33
Publications
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611
Citations
Introduction

Publications

Publications (33)
Article
The combinatorial optimization literature contains a multitude of polynomially solvable special cases of the traveling salesman problem (TSP) which result from imposing certain combinatorial restrictions on the underlying distance matrices. Many of these special cases have the form of so-called four-point conditions: inequalities that involve the d...
Article
Full-text available
String similarity search and its variants are fundamental problems with many applications in areas such as data integration, data quality, computational linguistics, or bioinformatics. A plethora of methods have been developed over the last decades. Obtaining an overview of the state-of-the-art in this field is difficult, as results are published i...
Conference Paper
This paper outlines the design of a bit-parallel, multi-string algorithm for high-similarity string comparison. We present it in the framework for the longest common subsequence (LCS) problem developed by the author in [31]. The algorithm is based on a bit-parallel LCS algorithm by Crochemore et al. [14].
Article
A deterministic BSP algorithm for constructing the suffix array of a given string is presented, based on a technique which we call accelerated sampling. It runs in optimal O(n/p) local computation and communication, and requires a near optimal O(log log p) synchronisation steps. The algorithm provides an improvement over the synchronisation costs o...
Article
Conserved noncoding sequences (CNSs) in DNA are reliable pointers to regulatory elements controlling gene expression. Using a comparative genomics approach with four dicotyledonous plant species (Arabidopsis thaliana, papaya [Carica papaya], poplar [Populus trichocarpa], and grape [Vitis vinifera]), we detected hundreds of CNSs upstream of Arabidop...
Conference Paper
A grammar-compressed (GC) string is a string generated by a context-free grammar. This compression model includes LZ78 and LZW compression as a special case. We consider the longest common subsequence problem and the local subsequence recognition problem on a GC-text against a plain pattern. We show that, surprisingly, both problems can be solved i...
Article
Full-text available
The notion of a boundary graph property was recently introduced as a relaxation of that of a minimal property and was applied to several problems of both algorithmic and combinatorial nature. In the present paper, we first survey recent results related to this notion and then apply it to two algorithmic graph problems: Hamiltonian cycle and vertexk...
Article
Full-text available
Identification of regulatory sequences within non-coding regions of DNA is an essential step towards elucidation of gene networks. This approach constitutes a major challenge, however, as only a very small fraction of non-coding DNA is thought to contribute to gene regulation. The mapping of regulatory regions traditionally involves the laborious c...
Conference Paper
Bulk-synchronous parallelism (BSP) is a simple and efficient paradigm for parallel algorithm design and analysis. In this paper, we present a new simple deterministic BSP algorithm for the classical problem of selecting the k-th smallest element from an array of size n, for a given k, on a parallel computer with p processors. Our algorithm is based...
Conference Paper
We study the computational complexity of the hamiltonian cycle problem in the class of graphs of vertex degree at most 3. Our goal is to distinguish boundary properties of graphs that make the problem difficult (NP-complete) in this domain. In the present paper, we discover the first boundary class of graphs for the hamiltonian cycle problem in sub...
Conference Paper
Full-text available
Monge matrices play a fundamental role in optimisation theory, graph and string algorithms. Distance multiplication of two Monge matrices of size n can be performed in time O(n 2). Motivated by applications to string algorithms, we introduced in previous works a subclass of Monge matrices, that we call simple unit-Monge matrices. We also gave a dis...
Conference Paper
In this paper, we show new parallel algorithms for a set of classical string comparison problems: computation of string alignments, longest common subsequences (LCS) or edit distances, and longest increasing subsequence computation. These problems have a wide range of applications, in particular in computational biology and signal processing. We di...
Conference Paper
The longest increasing subsequence (LIS) problem is a classical problem in theoretical computer science and mathematics. Most existing parallel algorithms for this problem have very restrictive slackness conditions which prevent scalability to large numbers of processors. Other algorithms are scalable, but not work-optimal w.r.t. the fastest sequen...
Article
Dot plots are a standard method for local comparison of biological sequences. In a dot plot, a substring to substring distance is computed for all pairs of fixed-size windows in the input strings. Commonly, the Hamming distance is used since it can be computed in linear time. However, the Hamming distance is a rather crude measure of string similar...
Conference Paper
In our previous work, we introduced the concept of semilocal string comparison, and developed for it an efficient method called the seaweed algorithm. In the current paper, we introduce its extension, called the periodic seaweed algorithm. The new algorithm allows efficient exploitation of the periodic structure in one of the input strings. By appl...
Article
Computing string or sequence alignments is a classical method of comparing strings and has applications in many areas of computing, such as signal processing and bioinformatics. Semi-local string alignment is a recent generalisation of this method, in which the alignment of a given string and all substrings of another string are computed simultaneo...
Article
The Metric Traveling Salesman Problem (TSP) is a classical NP-hard optimization problem. The double-tree shortcutting method for Metric TSP yields an exponentially-sized space of TSP tours, each of which approximates the optimal solution within at most a factor of 2. We consider the problem of finding among these tours the one that gives the closes...
Article
For two strings a, b of lengths m, n, respectively, the longest common subsequence (LCS) problem consists in comparing a and b by computing the length of their LCS. In this paper, we define a generalisation, called “the all semi-local LCS problem”, where each string is compared against all substrings of the other string, and all prefixes of each st...
Article
Full-text available
The Metric Traveling Salesman Problem (TSP) is a classical NP-hard optimization problem. The double-tree shortcutting method for Metric TSP yields an exponentially-sized space of TSP tours, each of which approximates the optimal solution within at most a factor of 2. We consider the problem of finding among these tours the one that gives the closes...
Article
Full-text available
The Metric Traveling Salesman Problem (TSP) is a classical NP-hard optimization problem. The double-tree shortcutting method for Metric TSP yields an exponentially-sized space of TSP tours, each of which approximates the optimal solution within at most a factor of 2. We consider the problem of finding among these tours the one that gives the closes...
Article
A classical measure of string comparison is given by the longest common subsequence (LCS) problem on a pair of strings. We consider its generalisation, called the semi-local LCS problem, which arises naturally in many string-related problems. The semi-local LCS problem asks for the LCS scores for each of the input strings against every substring of...
Article
Computation on compressed strings is one of the key approaches to processing massive data sets. We consider local subsequence recognition problems on strings compressed by straight-line programs (SLP), which is closely related to Lempel--Ziv compression. For an SLP-compressed text of length $\bar m$, and an uncompressed pattern of length $n$, C{\'e...
Conference Paper
The Metric Traveling Salesman Problem (TSP) is a classical NP-hard optimization problem. The double-tree shortcutting method for Metric TSP yields an exponential-sized space of TSP tours, each of which is a 2-approximation to the exact solution. We consider the problem of minimum-weight double-tree shortcutting, for which Burkard et al. gave an alg...
Conference Paper
Full-text available
The Travelling Salesman Problem (TSP) is a classical NP-hard optimisation problem. There exist, however, special cases of the TSP that can be solved in polynomial time. Many of the well-known TSP special cases have been characterized by imposing special four-point conditions on the underlying distance matrix. Probably the most famous of these speci...
Conference Paper
This paper presents performance results for parallel algorithms that compute the longest common subsequence of two strings. This algorithm is a representative of a class of algorithms that compute string to string distances and has computational complexity O(n 2). The parallel algorithm uses a variable grid size, runs in O(p) supersteps (synchroniz...
Conference Paper
For two strings a, b, the longest common subsequence (LCS) problem consists in comparing a and b by computing the length of their LCS . In a previous paper, we defined a generalisation, called “the all semi-local LCS problem”, for which we proposed an efficient output representation and an efficient algorithm. In this paper, we consider a restricti...
Article
We present lower bounds on the amount of communication that matrix multiplication algorithms must perform on a distributed-memory parallel computer. We denote the number of processors by P and the dimension of square matrices by n. We show that the most widely used class of algorithms, the so-called two-dimensional (2D) algorithms, are optimal, in...
Article
The Bulk Synchronous model of parallel programming has proved to be a successful paradigm for developing portable, scalable, high performance software. Originally developed for use with traditional supercomputers, it was later applied to networks of workstations. Following the emergence of grid computing, new programming models are needed to exploi...
Conference Paper
The model of bulk-synchronous parallel (BSP) computation is an emerging paradigm of general-purpose parallel computing. In this paper, we consider the parallel complexity of two matrix problems: Gaussian elimination with pairwise pivoting, We develop a unified approach to both problems, and a new communication-efficient BSP algorithm for their solu...
Article
For two strings a, b of lengths m, n respectively, the longest common subsequence (LCS) problem consists in comparing a and b by computing the length of their LCS. In a previous paper, we defined a generalisation, called "the all semi-local LCS problem", for which we proposed an efficient geometric output representation, and an efficient algorithm...
Article
For two strings a, b of lengths m, n respectively, the longest common subsequence (LCS) problem consists in comparing a and b by computing the length of their LCS. In previous papers, we defined a generalisation, called "the all semi-local LCS problem", for which we proposed an ecient geometric output representation, and an ecient method based on f...

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