Related papers: A framework for cost-constrained genome rearrangem…
We introduce a generalization of the well known graph (vertex) coloring problem, which we call the problem of \emph{component coloring of graphs}. Given a graph, the problem is to color the vertices using minimum number of colors so that…
Most state-of-the-art motion segmentation algorithms draw their potential from modeling motion differences of local entities such as point trajectories in terms of pairwise potentials in graphical models. Inference in instances of minimum…
The circular median problem in the Double-Cut-and-Join (DCJ) distance asks to find, for three given genomes, a fourth circular genome that minimizes the sum of the mutual distances with the three other ones. This problem has been shown to…
The minimum cost lifted multicut approach has proven practically good performance in a wide range of applications such as image decomposition, mesh segmentation, multiple object tracking, and motion segmentation. It addresses such problems…
The complexity of a reasoning task over a graphical model is tied to the induced width of the underlying graph. It is well-known that the conditioning (assigning values) on a subset of variables yields a subproblem of the reduced complexity…
In comparative genomics, the rearrangement distance between two genomes (equal the minimal number of genome rearrangements required to transform them into a single genome) is often used for measuring their evolutionary remoteness.…
We investigate problems addressing combined connectivity augmentation and orientations settings. We give a polynomial-time 6-approximation algorithm for finding a minimum cost subgraph of an undirected graph $G$ that admits an orientation…
We consider the problem of detecting multiple changepoints in large data sets. Our focus is on applications where the number of changepoints will increase as we collect more data: for example in genetics as we analyse larger regions of the…
The reconstruction of the history of evolutionary genome-wide events among a set of related organisms is of great biological interest. A simplified model that captures only content modifying operations was introduced recently. It allows the…
We consider three variants of the problem of finding a maximum weight restricted $2$-matching in a subcubic graph $G$. (A $2$-matching is any subset of the edges such that each vertex is incident to at most two of its edges.) Depending on…
We address the problem of finding the minimum decomposition of a permutation in terms of transpositions with non-uniform cost. For arbitrary non-negative cost functions, we describe polynomial-time, constant-approximation decomposition…
Suppose we are given a bipartite graph that admits a perfect matching and an adversary may delete any edge from the graph with the intention of destroying all perfect matchings. We consider the task of adding a minimum cost edge-set to the…
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.…
The d-Cut problem is to decide if a graph has an edge cut such that each vertex has at most d neighbours at the opposite side of the cut. If $d=1$, we obtain the intensively studied Matching Cut problem. The d-Cut problem has been studied…
The computation of genomic distances has been a very active field of computational comparative genomics over the last 25 years. Substantial results include the polynomial-time computability of the inversion distance by Hannenhalli and…
Editing a graph into a disjoint union of clusters is a standard optimization task in graph-based data clustering. Here, complementing classic work where the clusters shall be cliques, we focus on clusters that shall be 2-clubs, that is,…
The Minimum Coloring Cut Problem is defined as follows: given a connected graph G with colored edges, find an edge cut E' of G (a minimal set of edges whose removal renders the graph disconnected) such that the number of colors used by the…
We study a general class of bicriteria network design problems. A generic problem in this class is as follows: Given an undirected graph and two minimization objectives (under different cost functions), with a budget specified on the first,…
We address the problem of finding the minimal number of block interchanges (exchange of two intervals) required to transform a duplicated linear genome into a tandem duplicated linear genome. We provide a formula for the distance as well as…
In the Euclidean $k$-means problems we are given as input a set of $n$ points in $\mathbb{R}^d$ and the goal is to find a set of $k$ points $C\subseteq \mathbb{R}^d$, so as to minimize the sum of the squared Euclidean distances from each…