Related papers: Snapping Graph Drawings to the Grid Optimally
We describe a linear-time algorithm that finds a planar drawing of every graph of a simple line or pseudoline arrangement within a grid of area O(n^{7/6}). No known input causes our algorithm to use area \Omega(n^{1+\epsilon}) for any…
Given a connected undirected weighted graph, we are concerned with problems related to partitioning the graph. First of all we look for the closest disconnected graph (the minimum cut problem), here with respect to the Euclidean norm. We…
We consider the task of drawing a graph on multiple horizontal layers, where each node is assigned a layer, and each edge connects nodes of different layers. Known algorithms determine the orders of nodes on each layer to minimize crossings…
Circular layouts are a popular graph drawing style, where vertices are placed on a circle and edges are drawn as straight chords. Crossing minimization in circular layouts is \NP-hard. One way to allow for fewer crossings in practice are…
There is a graph reduction system so that every optimal 1-planar graph can be reduced to an irreducible extended wheel graph, provided the reductions are applied such that the given graph class is preserved. A graph is optimal 1-planar if…
We discuss the problem of embedding graphs in the plane with restrictions on the vertex mapping. In particular, we introduce a technique for drawing planar graphs with a fixed vertex mapping that bounds the number of times edges bend. An…
We investigate the problem of constructing planar drawings with few bends for two related problems, the partially embedded graph problem---to extend a straight-line planar drawing of a subgraph to a planar drawing of the whole graph---and…
Can one reduce the size of a graph without significantly altering its basic properties? The graph reduction problem is hereby approached from the perspective of restricted spectral approximation, a modification of the spectral similarity…
Geometry diagram parsing plays a key role in geometry problem solving, wherein the primitive extraction and relation parsing remain challenging due to the complex layout and between-primitive relationship. In this paper, we propose a…
Drawings of highly connected (dense) graphs can be very difficult to read. Power Graph Analysis offers an alternate way to draw a graph in which sets of nodes with common neighbours are shown grouped into modules. An edge connected to the…
Graphs face challenges when dealing with massive datasets. They are essential tools for modeling interconnected data and often become computationally expensive. Graph embedding techniques, on the other hand, provide an efficient approach.…
Grid layouts are used by designers to spatially organise user interfaces when sketching and wireframing. However, their design is largely time consuming manual work. This is challenging due to combinatorial explosion and complex objectives,…
A straight-line drawing $\delta$ of a planar graph $G$ need not be plane, but can be made so by moving some of the vertices. Let shift$(G,\delta)$ denote the minimum number of vertices that need to be moved to turn $\delta$ into a plane…
Given a planar graph $G$, we consider drawings of $G$ in the plane where edges are represented by straight line segments (which possibly intersect). Such a drawing is specified by an injective embedding $\pi$ of the vertex set of $G$ into…
A greedily routable region (GRR) is a closed subset of $\mathbb R^2$, in which each destination point can be reached from each starting point by choosing the direction with maximum reduction of the distance to the destination in each point…
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…
The Planar Contraction problem is to test whether a given graph can be made planar by using at most k edge contractions. This problem is known to be NP-complete. We show that it is fixed-parameter tractable when parameterized by k.
Graph is an important data representation which appears in a wide diversity of real-world scenarios. Effective graph analytics provides users a deeper understanding of what is behind the data, and thus can benefit a lot of useful…
Problems in scientific computing, such as distributing large sparse matrix operations, have analogous formulations as hypergraph partitioning problems. A hypergraph is a generalization of a traditional graph wherein "hyperedges" may connect…
Graph modification problems, which aim to find a small set of modifications to a graph so that it satisfies a desired property, have been studied for several special graph classes. The literature is rather rich in NP-completeness results…