Related papers: Investigating the complexity of the double distanc…
In this paper, we examine the computational complexity of enumeration in certain genome rearrangement models. We first show that the Pairwise Rearrangement problem in the Single Cut-and-Join model (Bergeron, Medvedev, & Stoye, J. Comput.…
Technical signs of progress during the last decades has led to a situation in which the accumulation of genome sequence data is increasingly fast and cheap. The huge amount of molecular data available nowadays can help addressing new and…
The study of genetic map linearization leads to a combinatorial hard problem, called the {\em minimum breakpoint linearization} (MBL) problem. It is aimed at finding a linearization of a partial order which attains the minimum breakpoint…
Distance geometry is the study of the arrangements of points in space using only the mutual distances between them. The basic idea in this letter is to use distance geometry for thermodynamics studies of small clusters in the microcanonical…
The matching distance is a computationally tractable topological measure to compare multi-filtered simplicial complexes. We design efficient algorithms for approximating the matching distance of two bi-filtered complexes to any desired…
Path pairs are a modification of parallelogram polyominoes that provide yet another combinatorial interpretation of the Catalan numbers. More generally, the number of path pairs of length $n$ and distance $\delta$ corresponds to the…
Imagine that unlabelled tokens are placed on the edges of a graph, such that no two tokens are placed on incident edges. A token can jump to another edge if the edges having tokens remain independent. We study the problem of determining the…
We view the reconstruction of CAD models in the boundary representation (B-Rep) as the detection of geometric primitives of different orders, i.e. vertices, edges and surface patches, and the correspondence of primitives, which are…
A pedigree is a directed graph in which each vertex (except the founder vertices) has two parents. The main result in this paper is a construction of an infinite family of counter examples to a reconstruction problem on pedigrees, thus…
Maximum parsimony distance is a measure used to quantify the dissimilarity of two unrooted phylogenetic trees. It is NP-hard to compute, and very few positive algorithmic results are known due to its complex combinatorial structure. Here we…
We describe new approaches for distances between pairs of 2-dimensional surfaces (embedded in 3-dimensional space) that use local structures and global information contained in inter-structure geometric relationships. We present algorithms…
Charge transfer in a DNA duplex chain is studied by constructing a system with virtual electrodes connected at the ends of each DNA strand. The systeym is described by the tight-binding model and its transport is analyzed by the transfer…
In many interesting cases the reconstruction of a correct phylogeny is blurred by high mutation rates and/or horizontal transfer events. As a consequence a divergence arises between the true evolutionary distances and the differences…
Several important algorithms for machine learning and data analysis use pairwise distances as input. On Riemannian manifolds these distances may be prohibitively costly to compute, in particular for large datasets. To tackle this problem,…
The Single Cut or Join (SCJ) operation on genomes, generalizing chromosome evolution by fusions and fissions, is the computationally simplest known model of genome rearrangement. While most genome rearrangement problems are already hard…
A pangenome captures the genetic diversity across multiple individuals simultaneously, providing a more comprehensive reference for genome analysis than a single linear genome, which may introduce allele bias. A widely adopted pangenome…
We propose a computational method to measure and visualize interrelationships among any number of DNA sequences allowing, for example, the examination of hundreds or thousands of complete mitochondrial genomes. An "image distance" is…
Various approaches to alignment-free sequence comparison are based on the length of exact or inexact word matches between two input sequences. Haubold {\em et al.} (2009) showed how the average number of substitutions between two DNA…
An RNA molecule is structured on several layers. The primary and most obvious structure is its sequence of bases, i.e. a word over the alphabet {A,C,G,U}. The higher structure is a set of one-to-one base-pairings resulting in a…
Genome assembly, the process of reconstructing a long genetic sequence by aligning and merging short fragments, or reads, is known to be NP-hard, either as a version of the shortest common superstring problem or in a Hamiltonian-cycle…