Approximate String Searching

1997 ◽  
Author(s):  
G.M. Landau ◽  
U. Vishkin
Keyword(s):  
Parallel Algorithms ◽  
Efficient Algorithm ◽  
Common Ancestor ◽  
Rooted Tree ◽  
Text String ◽  
String Searching ◽  
Lowest Common Ancestor ◽  
Input Form

Consider the string searching problem, where differences between characters of the pattern and characters of the text are allowed. Each difference is due to either a mismatch between a character of the text and a character of the pattern, or a superfluous character in the text, or a superfluous character in the pattern. Given a text of length n, a pattern of length m and an integer k, serial and parallel algorithms for finding all occurrences of the pattern in the text with at most k differences are presented. For completeness we also describe an efficient algorithm for preprocessing a rooted tree, so that queries requesting the lowest common ancestor of every pair of vertices in the tree can be processed quickly. Input form. Two arrays: A = a1., ...,am - the pattern, T = t1, ...,tn - the text and an integer k (≥ 1). In the present chapter we will be interested in finding all occurrences of the pattern string in the text string with at most k differences. Three types of differences are distinguished: (a) A character of the pattern corresponds to a different character of the text - a mismatch between the two characters. (Item 2 in Example 1, below.) (b) A character of the pattern corresponds to “no character” in the text. (Item 4). (c) A character of the text corresponds to “no character” in the pattern. (Item 6). Example 1. Let the text be abcdefghi , the pattern bxdyegh and k = 3. Let us see whether there is an occurrence with ≤ k differences that ends at the eighth location of the text. For this the following correspondence between bcdefgh and bxdyegh is proposed. 1. b (of the text) corresponds to b (of the pattern). 2. c to x. 3. d to d. 4. Nothing to y. 5. e to e. 6. f to nothing. 7. g to g. 8. h to h.

scholarly journals On the Distribution of Depths in Increasing Trees

10.37236/409 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Markus Kuba ◽  
Stephan Wagner
Keyword(s):  
Common Ancestor ◽  
Short Note ◽  
Bijective Proof ◽  
Lowest Common Ancestor ◽  
Recursive Trees

By a theorem of Dobrow and Smythe, the depth of the $k$th node in very simple families of increasing trees (which includes, among others, binary increasing trees, recursive trees and plane ordered recursive trees) follows the same distribution as the number of edges of the form $j-(j+1)$ with $j < k$. In this short note, we present a simple bijective proof of this fact, which also shows that the result actually holds within a wider class of increasing trees. We also discuss some related results that follow from the bijection as well as a possible generalization. Finally, we use another similar bijection to determine the distribution of the depth of the lowest common ancestor of two nodes.

FASTPAT: a fast and efficient algorithm for string searching in DNA sequences

1993 ◽  
Vol 9 (5) ◽  
pp. 541-545
Author(s):  
Prunella Nicola ◽  
Sabino Liuni ◽  
Marcella Attimonelli ◽  
Graziano Pasole
Keyword(s):  
Dna Sequences ◽  
Efficient Algorithm ◽  
String Searching

PARALLEL RANGE MINIMA ON COARSE GRAINED MULTICOMPUTERS

1999 ◽  
Vol 10 (04) ◽  
pp. 375-389
Author(s):  
H. MONGELLI ◽  
S. W. SONG
Keyword(s):  
Common Ancestor ◽  
Basic Problem ◽  
Coarse Grained ◽  
Time Range ◽  
Communication Overhead ◽  
Constant Number ◽  
Real Numbers ◽  
Graph Problems ◽  
Large N ◽  
Lowest Common Ancestor

Given an array of n real numbers A=(a0, a1, …, an-1), define MIN(i,j)= min {ai,…,aj}. The range minima problem consists of preprocessing array A such that queries MIN(i,j), for any 0≤i≤n-1 can be answered in constant time. Range minima is a basic problem that appears in many other important graph problems such as lowest common ancestor, Euler tour, etc. In this work we present a parallel algorithm under the CGM model (coarse grained multicomputer), that solves the range minima problem in O(n/p) time and constant number of communication rounds. The communication overhead involves the transmission of p numbers (independent of n). We show promising experimental results with speedup curves approximating the optimal for large n.

scholarly journals A scalable approach to computing representative lowest common ancestor in directed acyclic graphs

2013 ◽  
Vol 513 ◽  
pp. 25-37 ◽  
Author(s):  
Santanu Kumar Dash ◽  
Sven-Bodo Scholz ◽  
Stephan Herhut ◽  
Bruce Christianson
Keyword(s):  
Common Ancestor ◽  
Directed Acyclic Graphs ◽  
Acyclic Graphs ◽  
Lowest Common Ancestor

The lowest common ancestor problem on a tree with an unfixed root

1999 ◽  
Vol 119 (1-2) ◽  
pp. 125-130 ◽  
Author(s):  
Biing-Feng Wang ◽  
Jiunn-Nan Tsai ◽  
Yuan-Cheng Chuang
Keyword(s):  
Common Ancestor ◽  
Lowest Common Ancestor

scholarly journals Pangolin homology associated with 2019-nCoV

2020 ◽  
Author(s):  
Tao Zhang ◽  
Qunfu Wu ◽  
Zhigang Zhang
Keyword(s):  
Amino Acid ◽  
Intermediate Host ◽  
Common Ancestor ◽  
Whole Genome ◽  
Amino Acid Residues ◽  
Pathogenic Potential ◽  
Lowest Common Ancestor ◽  
Amino Acid Mutations ◽  
Genome Level ◽  
Novel Coronavirus

AbstractTo explore potential intermediate host of a novel coronavirus is vital to rapidly control continuous COVID-19 spread. We found genomic and evolutionary evidences of the occurrence of 2019-nCoV-like coronavirus (named as Pangolin-CoV) from dead Malayan Pangolins. Pangolin-CoV is 91.02% and 90.55% identical at the whole genome level to 2019-nCoV and BatCoV RaTG13, respectively. Pangolin-CoV is the lowest common ancestor of 2019-nCoV and RaTG13. The S1 protein of Pangolin-CoV is much more closely related to 2019-nCoV than RaTG13. Five key amino-acid residues involved in the interaction with human ACE2 are completely consistent between Pangolin-CoV and 2019-nCoV but four amino-acid mutations occur in RaTG13. It indicates Pangolin-CoV has similar pathogenic potential to 2019-nCoV, and would be helpful to trace the origin and probable intermediate host of 2019-nCoV.

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