Related papers: A fast algorithm for computing a planar support fo…
An instance of the super-stable matching problem with incomplete lists and ties is an undirected bipartite graph $G = (A \cup B, E)$, with an adjacency list being a linearly ordered list of ties. Ties are subsets of vertices equally good…
It has been recently shown that any graph of genus g>0 can be stochastically embedded into a distribution over planar graphs, with distortion Olog (g+1)) [Sidiropoulos, FOCS 2010]. This embedding can be computed in polynomial time, provided…
Given a $k$-node pattern graph $H$ and an $n$-node host graph $G$, the subgraph counting problem asks to compute the number of copies of $H$ in $G$. In this work we address the following question: can we count the copies of $H$ faster if…
We present an algorithm to support the dynamic embedding in the plane of a dynamic graph. An edge can be inserted across a face between two vertices on the face boundary (we call such a vertex pair linkable), and edges can be deleted. The…
In a rectilinear dual of a planar graph vertices are represented by simple rectilinear polygons and edges are represented by side-contact between the corresponding polygons. A rectilinear dual is called a cartogram if the area of each…
The Massive Parallel Computation (MPC) model is a theoretical framework for popular parallel and distributed platforms such as MapReduce, Hadoop, or Spark. We consider the task of computing a large matching or small vertex cover in this…
We investigate the two problems of computing the union join graph as well as computing the subset graph for acyclic hypergraphs and their subclasses. In the union join graph $G$ of an acyclic hypergraph $H$, each vertex of $G$ represents a…
In \emph{smooth orthogonal layouts} of planar graphs, every edge is an alternating sequence of axis-aligned segments and circular arcs with common axis-aligned tangents. In this paper, we study the problem of finding smooth orthogonal…
A measure for the visual complexity of a straight-line crossing-free drawing of a graph is the minimum number of lines needed to cover all vertices. For a given graph $G$, the minimum such number (over all drawings in dimension $d \in…
We consider straight line drawings of a planar graph $G$ with possible edge crossings. The \emph{untangling problem} is to eliminate all edge crossings by moving as few vertices as possible to new positions. Let $fix(G)$ denote the maximum…
In the area of beyond-planar graphs, i.e. graphs that can be drawn with some local restrictions on the edge crossings, the recognition problem is prominent next to the density question for the different graph classes. For 1-planar graphs,…
Given an input graph G and a node v in G, homogeneous network embedding (HNE) maps the graph structure in the vicinity of v to a compact, fixed-dimensional feature vector. This paper focuses on HNE for massive graphs, e.g., with billions of…
Let $G$ be a graph that is topologically embedded in the plane and let $\mathcal{A}$ be an arrangement of pseudolines intersecting the drawing of $G$. An aligned drawing of $G$ and $\mathcal{A}$ is a planar polyline drawing $\Gamma$ of $G$…
In this paper, we introduce a new approach for drawing diagrams that have applications in software visualization. Our approach is to use a technique we call confluent drawing for visualizing non-planar diagrams in a planar way. This…
Let $G = (V,E,w)$ be a weighted undirected graph on $|V| = n$ vertices and $|E| = m$ edges, let $k \ge 1$ be any integer, and let $\epsilon < 1$ be any parameter. We present the following results on fast constructions of spanners with…
A visualized graph is a powerful tool for data analysis and synthesis tasks. In this case, the task of visualization constitutes not only in displaying vertices and edges according to the graph representation, but also in ensuring that the…
Many of the classic graph problems cannot be solved in the Massively Parallel Computation setting (MPC) with strongly sublinear space per machine and $o(\log n)$ rounds, unless the 1-vs-2 cycles conjecture is false. This is true even on…
Given a graph $ G $ with $ n $ vertices and a set $ S $ of $ n $ points in the plane, a point-set embedding of $ G $ on $ S $ is a planar drawing such that each vertex of $ G $ is mapped to a distinct point of $ S $. A straight-line…
A $k$-matching cover of a graph $G$ is a union of $k$ matchings of $G$ which covers $V(G)$. A matching cover of $G$ is optimal if it consists of the fewest matchings of $G$. In this paper, we present an algorithm for finding an optimal…
Let $\mathcal{T}$ be a rooted and weighted tree, where the weight of any node is equal to the sum of the weights of its children. The popular Treemap algorithm visualizes such a tree as a hierarchical partition of a square into rectangles,…