Related papers: Investigating the complexity of the double distanc…
We address the problem of computing distances between rankings that take into account similarities between candidates. The need for evaluating such distances is governed by applications as diverse as rank aggregation, bioinformatics, social…
The NP-hard Metric Dimension problem is to decide for a given graph G and a positive integer k whether there is a vertex subset of size at most k that separates all vertex pairs in G. Herein, a vertex v separates a pair {u,w} if the…
Graph edit distance (GED) is a powerful and flexible graph matching paradigm that can be used to address different tasks in structural pattern recognition, machine learning, and data mining. In this paper, some new binary linear programming…
Persistence diagrams, combining geometry and topology for an effective shape description used in pattern recognition, have already proven to be an effective tool for shape representation with respect to a certainfiltering function.…
We propose a novel combination of methods that (i) portrays quantitative characteristics of a DNA sequence as an image, (ii) computes distances between these images, and (iii) uses these distances to output a map wherein each sequence is a…
Given an elementary chain of vertex set V, seen as a labelling of V by the set {1, ...,n=|V|}, and another discrete structure over $V$, say a graph G, the problem of common intervals is to compute the induced subgraphs G[I], such that $I$…
A matching is said to be disconnected if the saturated vertices induce a disconnected subgraph and induced if the saturated vertices induce a 1-regular graph. The disconnected and induced matching numbers are defined as the maximum…
An RNA sequence is a word over an alphabet on four elements $\{A,C,G,U\}$ called bases. RNA sequences fold into secondary structures where some bases match one another while others remain unpaired. Pseudoknot-free secondary structures can…
Let $SGL_n(\mathbb{F}_2)$ be the set of all invertible $n\times n$ symmetric matrices over the binary field $\mathbb{F}_2$. Let $\Gamma_n$ be the graph with the vertex set $SGL_n(\mathbb{F}_2)$ where a pair of matrices $\{A,B\}$ form an…
We provide, on an extensive dataset and using several different distances, confirmation of the hypothesis that CGR patterns are preserved along a genomic DNA sequence, and are different for DNA sequences originating from genomes of…
Phylogenetic networks are notoriously difficult to reconstruct. Here we suggest that it can be useful to view unknown genetic distance along edges in phylogenetic networks as analogous to unknown resistance in electric circuits. This…
In this work we study the interleaving distance between merge trees from a combinatorial point of view. We use a particular type of matching between trees to obtain a novel formulation of the distance. With such formulation, we tackle the…
Pedigrees, or family trees, are graphs of family relationships that are used to study inheritance. A fundamental problem in computational biology is to find, for a pedigree with $n$ individuals genotyped at every site, a set of…
In a graph, a matching cut is an edge cut that is a matching. Matching Cut is the problem of deciding whether or not a given graph has a matching cut, which is known to be NP-complete even when restricted to bipartite graphs. It has been…
Let D be an arbitrary subset of the natural numbers. For every n, let M(n;D) be the maximum of the cardinality of a set of Hamiltonian paths in the complete graph K_n such that the union of any two paths from the family contains a not…
We define the complexity of DNA sequences as the information content per nucleotide, calculated by means of some Lempel-Ziv data compression algorithm. It is possible to use the statistics of the complexity values of the functional regions…
Natural genomes sometimes encode two different proteins in staggered reading frames of the same DNA sequence. Despite the prevalence of these 'overlapping genes' across the tree of life, it remains unknown whether arbitrary protein pairs…
The double digest problem is a common NP-hard approach to constructing physical maps of DNA sequences. This paper presents a new approach called the enhanced double digest problem. Although this new problem is also NP-hard, it can be solved…
A binary linear error correcting codes represented by two code families Kronecker products sum are considered. The dimension and distance of new code is investigated. Upper and lower bounds of distance are obtained. Some examples are given.…
Genome sequencing is the basis for many modern biological and medicinal studies. With recent technological advances, metagenomics has become a problem of interest. This problem entails the analysis and reconstruction of multiple DNA…