Related papers: An effective crossing minimisation heuristic based…
We present a thorough experimental evaluation of several crossing minimization heuristics that are based on the construction and iterative improvement of a planarization, i.e., a planar representation of a graph with crossings replaced by…
Finding optimal matchings in dense graphs is of general interest and of particular importance in social, transportation and biological networks. While developing optimal solutions for various matching problems is important, the running…
A new heuristic for rectilinear crossing minimization is proposed. It is based on the idea of iteratively repositioning nodes after a first initial graph drawing. The new position of a node is computed by casting rays from the node towards…
The limited connectivity of current and next-generation quantum annealers motivates the need for efficient graph-minor embedding methods. These methods allow non-native problems to be adapted to the target annealer's architecture. The…
The algorithm of Gutwenger et al. to insert an edge $e$ in linear time into a planar graph $G$ with a minimal number of crossings on $e$, is a helpful tool for designing heuristics that minimize edge crossings in drawings of general graphs.…
We propose a novel optimization-based approach to embedding heterogeneous high-dimensional data characterized by a graph. The goal is to create a two-dimensional visualization of the graph structure such that edge-crossings are minimized…
Drawing graphs with the minimum number of crossings is a classical problem that has been studied extensively. Many restricted versions of the problem have been considered. For example, bipartite graphs can be drawn such that the two sets in…
A dominating set of a graph $\mathcal{G=(V, E)}$ is a subset of vertices $S\subseteq\mathcal{V}$ such that every vertex $v\in \mathcal{V} \setminus S$ outside the dominating set is adjacent to a vertex $u\in S$ within the set. The minimum…
An effective way to reduce clutter in a graph drawing that has (many) crossings is to group edges that travel in parallel into \emph{bundles}. Each edge can participate in many such bundles. Any crossing in this bundled graph occurs between…
Given a connected, undirected graph whose edges are labelled (or coloured), the minimum labelling spanning tree (MLST) problem seeks a spanning tree whose edges have the smallest number of distinct labels (or colours). In recent work, the…
Graph embedding is a fundamental problem of mapping nodes of a guest graph into a host graph while minimizing the distance distortion, with broad applications, including virtual network embeddings into physical topologies, VLSI design, or…
The crossing resolution of a non-planar drawing of a graph is the value of the minimum angle formed by any pair of crossing edges. Recent experiments have shown that the larger the crossing resolution is, the easier it is to read and…
We consider the minimization of edge-crossings in geometric drawings of graphs $G=(V, E)$, i.e., in drawings where each edge is depicted as a line segment. The respective decision problem is NP-hard [Bienstock, '91]. In contrast to theory…
A* is a classic and popular method for graphs search and path finding. It assumes the existence of a heuristic function $h(u,t)$ that estimates the shortest distance from any input node $u$ to the destination $t$. Traditionally, heuristics…
Neural network ensembling is a common and robust way to increase model efficiency. In this paper, we propose a new neural network ensemble algorithm based on Audibert's empirical star algorithm. We provide optimal theoretical minimax bound…
In this paper, we introduce a novel star partitioning problem for simple connected graphs $G=(V,E)$. The goal is to find a partition of the edges into stars that minimizes the maximum number of stars a node is contained in while…
This paper presents and experiments approaches to solve a new bi-objective routing problem called the ring star problem. It consists of locating a simple cycle through a subset of nodes of a graph while optimizing two kinds of cost. The…
In the Minimum Common String Partition Problem (MCSP), we are given two strings on input, and we want to partition both into the same collection of substrings, minimizing the number of the substrings in the partition. This combinatorial…
Fixed parameter tractable algorithms for bounded treewidth are known to exist for a wide class of graph optimization problems. While most research in this area has been focused on exact algorithms, it is hard to find decompositions of…
We consider the problem of embedding the nodes of a hypergraph into Euclidean space under the assumption that the interactions arose through closeness to unknown hyperedge centres. In this way, we tackle the inverse problem associated with…