Related papers: Algorithms for Tverberg's theorem via centerpoint …
An exact algorithm is presented for solving edge weighted graph partitioning problems. The algorithm is based on a branch and bound method applied to a continuous quadratic programming formulation of the problem. Lower bounds are obtained…
In 1989 H. Tverberg proposed a quite general conjecture in Discrete geometry, which could be considered as the common basis for many results in Combinatorial geometry and at the same time as a discrete analogue of the common transversal…
Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets.…
We consider the Minimum Convex Partition problem: Given a set P of n points in the plane, draw a plane graph G on P, with positive minimum degree, such that G partitions the convex hull of P into a minimum number of convex faces. We show…
Recently, Adiprasito et al. have initiated the study of the so-called no-dimensional Tverberg problem. This problem can be informally stated as follows: Given $n\geq k$, partition an $n$-point set in Euclidean space into $k$ parts such that…
The graph partitioning problem is a well-known NP-hard problem. In this paper, we formulate a 0-1 quadratic integer programming model for the graph partitioning problem with vertex weight constraints and fixed vertex constraints, and…
This paper discusses Tverberg-type theorems with coordinate constraints (i.e., versions of these theorems where all points lie within a subset $S \subset \mathbb{R}^d$ and the intersection of convex hulls is required to have a non-empty…
Many problems in computational geometry are not stated in graph-theoretic terms, but can be solved efficiently by constructing an auxiliary graph and performing a graph-theoretic algorithm on it. Often, the efficiency of the algorithm…
In this paper we consider some results on intersection between rays and a given family of convex, compact sets. These results are similar to the center point theorem, and Tverberg's theorem on partitions of a point set.
We study the k-median and k-center problems in probabilistic graphs. We analyze the hardness of these problems, and propose several algorithms with improved approximation ratios compared with the existing proposals.
We introduce a generalization of the Euclidean algorithm for rings equipped with an involution, and completely enumerate all isomorphism classes of orders over definite, rational quaternion algebras equipped with an orthogonal involution…
Graph theoretical problems based on shortest paths are at the core of research due to their theoretical importance and applicability. This paper deals with the geodetic number which is a global measure for simple connected graphs and it…
There are many space subdivision and space partitioning techniques used in many algorithms to speed up computations. They mostly rely on orthogonal space subdivision, resp. using hierarchical data structures, e.g. BSP trees, quadtrees,…
Tverberg's theorem says that a set with sufficiently many points in $\mathbb{R}^d$ can always be partitioned into $m$ parts so that the $(m-1)$-simplex is the (nerve) intersection pattern of the convex hulls of the parts. In…
In recent years, important progress has been made in applying methods and techniques of convex optimization to many fields of applications such as location science, engineering, computational statistics, and computer science. In this paper,…
Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…
We design improved approximation algorithms for NP-hard graph problems by incorporating predictions (e.g., learned from past data). Our prediction model builds upon and extends the $\varepsilon$-prediction framework by Cohen-Addad, d'Orsi,…
We consider the classical minimum and maximum cut problems: find a partition of vertices of a graph into two disjoint subsets that minimize or maximize the sum of the weights of edges with endpoints in different subsets. It is known that if…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
Can we use machine learning to compress graph data? The absence of ordering in graphs poses a significant challenge to conventional compression algorithms, limiting their attainable gains as well as their ability to discover relevant…