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A new method for constructing self-referential tilings of Euclidean space from a graph directed iterated function system, based on a combinatorial structure we call a pre-tree, is introduced. In the special case that we refer to as…
In this paper we study the problem of designing a distributed graph visualization algorithm for large graphs. The algorithm must be simple to implement and the computing infrastructure must not require major hardware or software…
Threshold graphs are a prevalent and widely studied class of simple graphs. They have several equivalent definitions which makes them a go-to class for finding examples and counter examples when testing and learning. This versatility has…
We introduce the notion of balance for directed graphs: a weighted directed graph is $\alpha$-balanced if for every cut $S \subseteq V$, the total weight of edges going from $S$ to $V\setminus S$ is within factor $\alpha$ of the total…
The recent proliferation of publicly available graph-structured data has sparked an interest in machine learning algorithms for graph data. Since most traditional machine learning algorithms assume data to be tabular, embedding algorithms…
This paper introduces the Strain Elevation Tension Spring embedding (SETSe) algorithm, a graph embedding method that uses a physics model to create node and edge embeddings in undirected attribute networks. Using a low-dimensional…
To solve many problems on graphs, graph traversals are used, the usual variants of which are the depth-first search and the breadth-first search. Implementing a graph traversal we consequently reach all vertices of the graph that belong to…
Graph embedding is the major technique which is used to map guest graph into host graph. In architecture simulation, graph embedding is said to be one of the strongest application for the execution of parallel algorithm and simulation of…
Neural networks are powerful function estimators, leading to their status as a paradigm of choice for modeling structured data. However, unlike other structured representations that emphasize the modularity of the problem -- e.g., factor…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
Graph embedding is a popular algorithmic approach for creating vector representations for individual vertices in networks. Training these algorithms at scale is important for creating embeddings that can be used for classification, ranking,…
In this paper, we propose a new type of graph, denoted as "embedded-graph", and its theory, which employs a distributed representation to describe the relations on the graph edges. Embedded-graphs can express linguistic and complicated…
In this paper we describe a randomized algorithm which returns a maximal spanning forest of an unknown {\em weighted} undirected graph making $O(n)$ $\mathsf{CUT}$ queries in expectation. For weighted graphs, this is optimal due to a result…
Acyclic and cyclic orientations of an undirected graph have been widely studied for their importance: an orientation is acyclic if it assigns a direction to each edge so as to obtain a directed acyclic graph (DAG) with the same vertex set;…
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…
Most of the common graph layout principles (a.k.a. "aesthetics") on which many graph drawing algorithms are based are easy to define and to perceive. For example, the number of pairs of edges that cross each other, how symmetric a drawing…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
Greedy embedding (or drawing) is a simple and efficient strategy to route messages in wireless sensor networks. For each source-destination pair of nodes s, t in a greedy embedding there is always a neighbor u of s that is closer to t…
We obtain new parameterized algorithms for the classical problem of determining whether a directed acyclic graph admits an upward planar drawing. Our results include a new fixed-parameter algorithm parameterized by the number of sources, an…
We introduce new distance measures for comparing straight-line embedded graphs based on the Fr\'echet distance and the weak Fr\'echet distance. These graph distances are defined using continuous mappings and thus take the combinatorial…