Longest property-preserved common factor

In this paper we introduce a new family of string processing problems. We are given two or more strings and we are asked to compute a factor common to all strings that preserves a specific property and has maximal length. Here we consider two fundamental string properties: square-free factors and periodic factors under two different settings, one per property. In the first setting, we are given a string x and we are asked to construct a data structure over x answering the following type of on-line queries: given string y, find a longest square-free factor common to x and y. In the second setting, we are given k strings and an integer 1 < k’ ≤ k and we are asked to find a longest periodic factor common to at least k’ strings. We present linear-time solutions for both settings. We anticipate that our paradigm can be extended to other string properties

Finding Maximal 2-Dimensional Palindromes

This paper extends the problem of palindrome searching into a higher dimension, addressing two definitions of 2D palindromes. The first definition implies a square, while the second definition (also known as a centrosymmetric factor), can be any rectangular shape. We describe two algorithms for searching a 2D text for maximal palindromes, one for each type of 2D palindrome. The first algorithm is optimal; it runs in linear time, on par with Manacher\u27s linear time 1D palindrome algorithm. The second algorithm searches a text of size n_1 x n_2 (n_1 >= n_2) in O(n_2) time for each of its n_1 x n_2 positions. Since each position may have up to O(n_2) maximal palindromes centered at that location, the second result is also optimal in terms of the worst-case output size

Using codes in place of DNA Sample in Databases to reduce Storage

Biological data mainly comprises of Deoxyribonucleic acid (DNA) and protein sequences. These arethe biomolecules that are present in all cells of human beings. Due to the self-replicating property ofDNA, it is a key constituent of genetic material that exists in all breathing creatures. This biomolecule(DNA) comprehends the genetic material obligatory for the operational and expansion of all personifiedlives. To save DNA data of a single person we require 10CD-Rom's. In this paper, A lossless three-phasecompression algorithm is presented for DNA sequences. In the first phase the dataset is segmentedhaving tetra groups and then the resultant genetic sequences are compressed in the form of uniquenumbers (e.g Array Index) and in the second phase binary code is generated on the bases of array indexnumbers and in the last phase the modified version of Run Length Encoding (RLE) is applied on thedataset.The newly proposed technique has been implemented and its performance is also measured on samples.It has achieved the best average compression ratio. After Storing different DNA Samples

Longest Property-Preserved Common Factor

International audienceIn this paper we introduce a new family of string processing problems. We are given two or more strings and we are asked to compute a factor common to all strings that preserves a specific property and has maximal length. Here we consider three fundamental string properties: square-free factors, periodic factors, and palindromic factors under three different settings, one per property. In the first setting, we are given a string x and we are asked to construct a data structure over x answering the following type of on-line queries: given string y, find a longest square-free factor common to x and y. In the second setting, we are given k strings and an integer 1 < k ≤ k and we are asked to find a longest periodic factor common to at least k strings. In the third setting, we are given two strings and we are asked to find a longest palindromic factor common to the two strings. We present linear-time solutions for all settings. We anticipate that our paradigm can be extended to other string properties or settings

28th Annual Symposium on Combinatorial Pattern Matching : CPM 2017, July 4-6, 2017, Warsaw, Poland

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