Related papers: A first efficient algorithm for enumerating all th…
Over the last years the vertex enumeration problem of polyhedra has seen a revival in the study of metabolic networks, which increased the demand for efficient vertex enumeration algorithms for high-dimensional polyhedra given by…
We focus on two central themes in this dissertation. The first one is on decomposing polytopes and polynomials in ways that allow us to perform nonlinear optimization. We start off by explaining important results on decomposing a polytope…
Finding an exact maximum distance of two points in the given set is a fundamental computational problem which is solved in many applications. This paper presents a fast, simple to implement and robust algorithm for finding this maximum…
To compute solutions of sparse polynomial systems efficiently we have to exploit the structure of their Newton polytopes. While the application of polyhedral methods naturally excludes solutions with zero components, an irreducible…
We present an algorithmic framework for computing anti-chains of maximum size in geometric posets. Specifically, posets in which the entities are geometric objects, where comparability of two entities is implicitly defined but can be…
Neighborly polytopes are those that maximize the number of faces in each dimension among all polytopes with the same number of vertices. Despite their extremal properties they form a surprisingly rich class of polytopes, which has been…
In this paper, we study the many-to-many matching problem on planar point sets with integer coordinates: Given two disjoint sets $R,B \subset [\Delta]^2$ with $|R|+|B|=n$, the goal is to select a set of edges between $R$ and $B$ so that…
The correlations arising from sequential measurements on a single quantum system form a polytope. This is defined by the arrow-of-time (AoT) constraints, meaning that future choices of measurement settings cannot influence past outcomes. We…
The enumeration of minimal connected dominating sets is known to be notoriously hard for general graphs. Currently, it is only known that the sets can be enumerated slightly faster than $\mathcal{O}^{*}(2^n)$ and the algorithm is highly…
Enumeration algorithms have been one of recent hot topics in theoretical computer science. Different from other problems, enumeration has many interesting aspects, such as the computation time can be shorter than the total output size, by…
We establish the optimal nonergodic sublinear convergence rate of the proximal point algorithm for maximal monotone inclusion problems. First, the optimal bound is formulated by the performance estimation framework, resulting in an infinite…
In multiobjective optimization, the result of an optimization algorithm is a set of efficient solutions from which the decision maker selects one. It is common that not all the efficient solutions can be computed in a short time and the…
We consider the problem of finding all allowed edges in a bipartite graph $G=(V,E)$, i.e., all edges that are included in some maximum matching. We show that given any maximum matching in the graph, it is possible to perform this…
We propose faster algorithms for the following three optimization problems on $n$ collinear points, i.e., points in dimension one. The first two problems are known to be NP-hard in higher dimensions. 1- Maximizing total area of disjoint…
The odd-red bipartite perfect matching problem asks to find a perfect matching containing an odd number of red edges in a given red-blue edge-colored bipartite graph. While this problem lies in $\mathsf{P}$, its polyhedral structure remains…
New algorithms are devised for finding the maxima of multidimensional point samples, one of the very first problems studied in computational geometry. The algorithms are very simple and easily coded and modified for practical needs. The…
It is known that point searching in basic semialgebraic sets and the search for globally minimal points in polynomial optimization tasks can be carried out using $(s\,d)^{O(n)}$ arithmetic operations, where $n$ and $s$ are the numbers of…
This paper examines a common extension of k-medoids and k-median clustering in the case of a two-dimensional Pareto front, as generated by bi-objective optimization approaches. A characterization of optimal clusters is provided, which…
In this paper, we are concerned with a worst-case complexity analysis of a-posteriori algorithms for unconstrained multiobjective optimization. Specifically, we propose an algorithmic framework that generates sets of points by means of…
Enumerating matchings is a classical problem in the field of enumeration algorithms. There are polynomial-delay enumeration algorithms for several settings, such as enumerating perfect matchings, maximal matchings, and (weighted) matchings…