Related papers: Drawing Graphs within Restricted Area
The maximal graph Dirichlet problem asks whether there exists a spacelike graph, in a semi-Euclidean space, with a given boundary and with mean curvature everywhere zero. We prove the existence of solutions to this problem under certain…
In this paper, we consider the problem of designing cut sparsifiers and sketches for directed graphs. To bypass known lower bounds, we allow the sparsifier/sketch to depend on the balance of the input graph, which smoothly interpolates…
In this paper, we study the exact learning problem for weighted graphs, where we are given the vertex set, $V$, of a weighted graph, $G=(V,E,w)$, but we are not given $E$. The problem, which is also known as graph reconstruction, is to…
The parametric geometry of numbers has allowed to visualize the simultaneous approximation properties of a collection of real numbers through the combined graph of the related successive minima functions. Several inequalities among…
Massive sizes of real-world graphs, such as social networks and web graph, impose serious challenges to process and perform analytics on them. These issues can be resolved by working on a small summary of the graph instead . A summary is a…
We introduce a general class of algorithms and supply a number of general results useful for analysing these algorithms when applied to regular graphs of large girth. As a result, we can transfer a number of results proved for random…
A matching in a graph is uniquely restricted if no other matching covers exactly the same set of vertices. We establish tight lower bounds on the maximum size of a uniquely restricted matching in terms of order, size, and maximum degree.
We study the problem of generating graphs with prescribed degree sequences for bipartite, directed, and undirected networks. We first propose a sequential method for bipartite graph generation and establish a necessary and sufficient…
Graphs are ubiquitous in encoding relational information of real-world objects in many domains. Graph generation, whose purpose is to generate new graphs from a distribution similar to the observed graphs, has received increasing attention…
In this thesis we consider ordered graphs (that is, graphs with a fixed linear ordering on their vertices). We summarize and further investigations on the number of edges an ordered graph may have while avoiding a fixed forbidden ordered…
In this paper, we study tradeoffs between curve complexity and area of Right Angle Crossing drawings (RAC drawings), which is a challenging theoretical problem in graph drawing. Given a graph with $n$ vertices and $m$ edges, we provide a…
Graphs and networks are common ways of depicting biological information. In biology, many different biological processes are represented by graphs, such as regulatory networks, metabolic pathways and protein--protein interaction networks.…
Computing the diameter of a graph, i.e. the largest distance, is a fundamental problem that is central in fine-grained complexity. In undirected graphs, the Strong Exponential Time Hypothesis (SETH) yields a lower bound on the time vs.…
Uncertain graphs are prevalent in several applications including communications systems, biological databases and social networks. The ever increasing size of the underlying data renders both graph storage and query processing extremely…
We consider the problem of sampling from data defined on the nodes of a weighted graph, where the edge weights capture the data correlation structure. As shown recently, using spectral graph theory one can define a cut-off frequency for the…
Consider the setting of \emph{randomly weighted graphs}, namely, graphs whose edge weights are chosen independently according to probability distributions with finite support over the non-negative reals. Under this setting, properties of…
We present faster algorithms for approximate maximum flow in undirected graphs with good separator structures, such as bounded genus, minor free, and geometric graphs. Given such a graph with $n$ vertices, $m$ edges along with a recursive…
The degree-diameter problem asks for the maximum number of vertices in a graph with maximum degree $\Delta$ and diameter $k$. For fixed $k$, the answer is $\Theta(\Delta^k)$. We consider the degree-diameter problem for particular classes of…
We examine the Maximum Independent Set Problem in an undirected graph. The main result is that this problem can be considered as the solving the same problem in a subclass of the weighted normal twin-orthogonal graphs. The problem is…
In this paper, the dynamics of heuristic algorithms for constructing small vertex covers (or independent sets) of finite-connectivity random graphs is analysed. In every algorithmic step, a vertex is chosen with respect to its vertex…