Algorithmica

We study the complexity of graph modification problems with respect to homomorphism-based colouring properties of edge-coloured graphs. A homomorphism from an edge-coloured graph G to an edge-coloured graph H is a vertex-mapping from G to H that ...$$${}^{}$

We revisit the online Unit Clustering and Unit Covering problems in higher dimensions: Given a set of n points in a metric space, that arrive one by one, Unit Clustering asks to partition the points into the minimum number of clusters (subsets) of ...${\mathbb{}}^{}$${}_{}$$\mathrm{}$${}^{\mathrm{}}$${\mathbb{}}^{}$$\mathbb{}$${}_{}$${\mathrm{}}^{}$

We introduce a new type of adversary for online graph problems thus allowing parametrized analysis of online algorithms with respect to a natural parameter. The new adversary is parameterized by a single integer $\kappa$, which upper bounds the number of ...$$$$$$$$$$$$${}_{}$$$

Directed Steiner Tree (DST) is a central problem in combinatorial optimization and theoretical computer science: Given a directed graph $G=(V,E)$ with edge costs $c\in {\mathbb{R}}_{\ge 0}^E$, a root $r\in V$ and k terminals $K\subseteq V$, we need to output the minimum-cost arborescence ...$$$$${}^{\mathrm{}}$${}_{}$$$${}_{}$${}^{\mathrm{}}$$$${}^{\mathrm{}}$${}^{\mathrm{}}$$$$\mathrm{}$$$

For a finite set V of elements, a confluent system is a set system $(V,\mathcal{C}\subseteq 2^V)$ such that every three sets $X,Y,Z\in \mathcal{C}$ with $Z\subseteq X\cap Y$ implies $X\cup Y\in \mathcal{C}$, where we call a set $C\in \mathcal{C}$ a component. We assume that two oracles ${\mathrm{L}}_1$ and ${\mathrm{L}}_2$ are available, where given two ...$$${\mathrm{}}_{\mathrm{}}$$\mathcal{}$$$$$${\mathrm{}}_{\mathrm{}}$$\mathcal{}$$$${\mathrm{}}^{}$$\mathcal{}$${}_{}{}_{}$$\mathcal{}$$$

Online routing in a planar embedded graph is central to a number of fields and has been studied extensively in the literature. For most planar graphs no O(1)-competitive online routing algorithm exists. A notable exception is the Delaunay ...$$

This paper is concerned with the $1||\sum p_j{U}_j$ problem, the problem of minimizing the total processing time of tardy jobs on a single machine. This is not only a fundamental scheduling problem, but also an important problem from a theoretical point of ...$$

We study the relationship between the competitive ratio and the tail distribution of randomized online problems. To this end, we identify a broad class of online problems for which the existence of a randomized online algorithm with constant ...$\mathrm{}$

The two weighted graph problems Node Multiway Cut (NMC) and Subset Feedback Vertex Set (SFVS) both ask for a vertex set of minimum total weight, that for NMC disconnects a given set of terminals, and for SFVS intersects all cycles containing a ...${\mathrm{}}^{{}^{\mathrm{}}}{}^{\mathrm{}}$${\mathrm{}}^{{}^{\mathrm{}}}{}^{\mathrm{}}$${}^{{}^{\mathrm{}}}$$\mathbb{}$

Sequence mappability is an important task in genome resequencing. In the (k, m)-mappability problem, for a given sequence T of length n, the goal is to compute a table whose ith entry is the number of indices $j\ne i$ such that the length-m substrings ...$\mathrm{}$$\mathrm{}$$$${}^{}{}^{}$${}^{\mathrm{}}$$\mathrm{}$$$$\mathrm{}$

Metric data plays an important role in various settings, for example, in metric-based indexing, clustering, classification, and approximation algorithms in general. Due to measurement error, noise, or an inability to completely gather all the data,...