Related papers: A census of graph-drawing algorithms based on gene…
A $d$-angulation is a planar map with faces of degree $d$. We present for each integer $d\geq 3$ a bijection between the class of $d$-angulations of girth $d$ (i.e., with no cycle of length less than $d$) and a class of decorated plane…
We generalise structure tree theory, which is based on removing finitely many edges, to removing finitely many vertices. This gives a significant generalization of Tutte's tree decomposition of 2-connected graphs into 3-connected blocks.…
A connected graph is 4-connected if it contains at least five vertices and removing any three of them does not disconnect it. A frequent preprocessing step in graph drawing is to decompose a plane graph into its 4-connected components and…
A traversal of a connected graph is a linear ordering of its vertices all of whose initial segments induce connected subgraphs. Traversals, and their refinements such as breadth-first and depth-first traversals, are computed by various…
We consider drawings of trees in which all edges incident to leaves can be extended to infinite rays without crossing, partitioning the plane into infinite convex polygons. Among all such drawings we seek the one maximizing the angular…
We present a graph-theoretic framework for constructing floor plans that support non-rectangular modules, with particular emphasis on L-shaped and T-shaped geometries. Unlike traditional approaches that primarily focus on rectangular…
We exploit a decomposition of graph traversals to give a novel characterization of depth-first and breadth-first traversals as universal constructions. Specifically, we introduce functors from two different categories of edge-ordered…
Motivated by performance optimization of large-scale graph processing systems that distribute the graph across multiple machines, we consider the balanced graph partitioning problem. Compared to the previous work, we study the…
We develop a framework for algorithms finding the diameter in graphs of bounded distance Vapnik-Chervonenkis dimension, in (parameterized) subquadratic time complexity. The class of bounded distance VC-dimension graphs is wide, including,…
Orthogonal graph drawing has many applications, e.g., for laying out UML diagrams or cableplans. In this paper, we present a new pipeline that draws multigraphs orthogonally, using few bends, few crossings, and small area. Our pipeline…
We propose a new algorithm for finding the center of a graph, as well as the rank of each node in the hierarchy of distances to the center. In other words, our algorithm allows to partition the graph according to nodes distance to the…
We consider a new semidefinite programming relaxation for directed edge expansion, which is obtained by adding triangle inequalities to the reweighted eigenvalue formulation. Applying the matrix multiplicative weight update method to this…
We derive a new lower bound for the bandwidth of a graph that is based on a new lower bound for the minimum cut problem. Our new semidefinite programming relaxation of the minimum cut problem is obtained by strengthening the known…
We compute the treewidth of a family of graphs we refer to as the glued grids, consisting of the stacked prism graphs and the toroidal grids. Our main technique is constructing strict brambles of large orders. We discuss connections to…
In this paper we show how to combine two algorithmic techniques to obtain linear time algorithms for various optimization problems on graphs, and present a subroutine which will be useful in doing so. The first technique is iterative…
The greedy leaf removal (GLR) procedure on a graph is an iterative removal of any vertex with degree one (leaf) along with its nearest neighbor (root). Its result has two faces: a residual subgraph as a core, and a set of removed roots.…
Given a persistence diagram with $n$ points, we give an algorithm that produces a sequence of $n$ persistence diagrams converging in bottleneck distance to the input diagram, the $i$th of which has $i$ distinct (weighted) points and is a…
This article presents a unified bijective scheme between planar maps and blossoming trees, where a blossoming tree is defined as a spanning tree of the map decorated with some dangling half-edges that enable to reconstruct its faces. Our…
In the past decades, many graph drawing techniques have been proposed for generating aesthetically pleasing graph layouts. However, it remains a challenging task since different layout methods tend to highlight different characteristics of…
The random greedy algorithm for constructing a large partial Steiner-Triple-System is defined as follows. Begin with a complete graph on $n$ vertices and proceed to remove the edges of triangles one at a time, where each triangle removed is…