Related papers: Genome assembly, from practice to theory: safe, co…
The Watson-Crick complementary properties of DNA make DNA a useful tool for the self-assembly of various target complexes. Concepts from graph theory can be used to model the self-assembling process in which the vertices of the graph…
Gene assembly is an intricate biological process that has been studied formally and modeled through string and graph rewriting systems. Recently, a restriction of the general (intramolecular) model, called simple gene assembly, has been…
This work describes a new algorithm for creating a superposition over the edge set of a graph, encoding a quantum sample of the random walk stationary distribution. The algorithm requires a number of quantum walk steps scaling as…
A crucial problem in genome assembly is the discovery and correction of misassembly errors in draft genomes. We develop a method that will enhance the quality of draft genomes by identifying and removing misassembly errors using paired…
The girth of a graph, i.e. the length of its shortest cycle, is a fundamental graph parameter. Unfortunately all known algorithms for computing, even approximately, the girth and girth-related structures in directed weighted $m$-edge and…
Palindromes are strings that read the same forward and backward. The computation of palindromic structures within strings is a fundamental problem in string algorithms, being motivated by potential applications in formal language theory and…
Assembly theory has received considerable attention in the recent past. Here we analyze the formal framework of this model and show that assembly pathways coincide with certain minimal hyperpaths in B-hypergraphs. This makes it possible to…
Within biology, it is of interest to construct DNA complexes of a certain shape. These complexes can be represented through graph theory, using edges to model strands of DNA joined at junctions, represented by vertices. Because guided…
A useful approach to the mathematical analysis of large-scale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational problems associated to finding decompositions…
The Consecutive-Ones Property (C1P) is a classical concept in discrete mathematics that has been used in several genomics applications, from physical mapping of contemporary genomes to the assembly of ancient genomes. A common issue in…
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…
In this paper, we provide polynomial-time algorithms for different extensions of the matching counting problem, namely maximal matchings, path matchings (linear forest) and paths, on graph classes of bounded clique-width. For maximal…
Given an undirected, weighted graph, with $n$ vertices and $m$ edges, and two special vertices $s$ and $t$, the problem is to find the shortest path between them. We give two bounded-error quantum algorithms with improved runtime in the…
We initiate the study of a fundamental combinatorial problem: Given a capacitated graph $G=(V,E)$, find a shortest walk ("route") from a source $s\in V$ to a destination $t\in V$ that includes all vertices specified by a set…
Branched junction molecule assembly of DNA nanostructures, pioneered by Seeman's laboratory in the 1980s, has become increasingly sophisticated, as have the assembly targets. A critical design step is finding minimal sets of branched…
Recent work identified the fundamental limits on the information requirements in terms of read length and coverage depth required for successful de novo genome reconstruction from shotgun sequencing data, based on the idealistic assumption…
The formal version of our work has been published in BMC Bioinformatics and can be found here: http://www.biomedcentral.com/1471-2105/13/S6/S1 Motivation: To tackle the problem of huge memory usage associated with de Bruijn graph-based…
The Maximum Matching problem has a quantum query complexity lower bound of $\Omega(n^{3/2})$ for graphs on $n$ vertices represented by an adjacency matrix. The current best quantum algorithm has the query complexity $O(n^{7/4})$, which is…
Dense subgraphs of sparse graphs (communities), which appear in most real-world complex networks, play an important role in many contexts. Computing them however is generally expensive. We propose here a measure of similarities between…
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…