Related papers: The Binary Perfect Phylogeny with Persistent chara…
The most fundamental problem considered in algorithms for text processing is pattern matching: given a pattern $p$ of length $m$ and a text $t$ of length $n$, does $p$ occur in $t$? Multiple versions of this basic question have been…
Phylogenetic networks generalise phylogenetic trees and allow for the accurate representation of the evolutionary history of a set of present-day species whose past includes reticulate events such as hybridisation and lateral gene transfer.…
Perfect Matching-Cut is the problem of deciding whether a graph has a perfect matching that contains an edge-cut. We show that this problem is NP-complete for planar graphs with maximum degree four, for planar graphs with girth five, for…
Best match graphs (BMGs) are a class of colored digraphs that naturally appear in mathematical phylogenetics and can be approximated with the help of similarity measures between gene sequences, albeit not without errors. The corresponding…
Microarrays are research tools used in gene discovery as well as disease and cancer diagnostics. Two prominent but challenging problems related to microarrays are the Border Minimization Problem (BMP) and the Border Minimization Problem…
Many complex questions in biology, physics, and mathematics can be mapped to the graph isomorphism problem and the closely related graph automorphism problem. In particular, these problems appear in the context of network visualization,…
We consider the phylogenetic tree reconstruction problem with insertions and deletions (indels). Phylogenetic algorithms proceed under a model where sequences evolve down the model tree, and given sequences at the leaves, the problem is to…
Various algorithms have been proposed for dictionary learning. Among those for image processing, many use image patches to form dictionaries. This paper focuses on whole-image recovery from corrupted linear measurements. We address the open…
A \emph{binary tanglegram} is a drawing of a pair of rooted binary trees whose leaf sets are in one-to-one correspondence; matching leaves are connected by inter-tree edges. For applications, for example, in phylogenetics, it is essential…
Tree containment problem is a fundamental problem in phylogenetic study, as it is used to verify a network model. It asks whether a given network contain a subtree that resembles a binary tree. The problem is NP-complete in general, even in…
Persistent homology is a tool that can be employed to summarize the shape of data by quantifying homological features. When the data is an object in $\mathbb{R}^d$, the (augmented) persistent homology transform ((A)PHT) is a family of…
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…
In this paper we resolve the complexity of the isomorphism problem on all but finitely many of the graph classes characterized by two forbidden induced subgraphs. To this end we develop new techniques applicable for the structural and…
Motivated by comparative genomics, Chen et al. [9] introduced the Maximum Duo-preservation String Mapping (MDSM) problem in which we are given two strings $s_1$ and $s_2$ from the same alphabet and the goal is to find a mapping $\pi$…
We study a delay-sensitive information flow problem where a source streams information to a sink over a directed graph G(V,E) at a fixed rate R possibly using multiple paths to minimize the maximum end-to-end delay, denoted as the…
Most of major algorithms for phylogenetic tree reconstruction assume that sequences in the analyzed set either do not have any offspring, or that parent sequences can maximally mutate into just two descendants. The graph resulting from such…
We have proved that for any pattern p the tail recursive program model of naive pattern matching may be automatically specialized w.r.t. the pattern p to a specialized version of the so-called KMP-algorithm, using the Higman-Kruskal…
Near-Periodic Patterns (NPP) are ubiquitous in man-made scenes and are composed of tiled motifs with appearance differences caused by lighting, defects, or design elements. A good NPP representation is useful for many applications including…
The ancestral sequence reconstruction problem is the inference, back in time, of the properties of common sequence ancestors from measured properties of contemporary populations. Standard algorithms for this problem assume independent…
The $H$-Coloring problem is a well-known generalization of the classical NP-complete problem $k$-Coloring where the task is to determine whether an input graph admits a homomorphism to the template graph $H$. This problem has been the…