When applying iterative compression to solve an optimization problem, we construct a smaller auxiliary graph from the input graph, solve the problem on this smaller graph, and then use the solution to solve the original problem. We present a variant of this approach in which the smaller graph inherits the connectivity properties of the original graph. This is especially useful when trying to so...

When applying iterative compression to solve an optimization problem, we construct a smaller auxiliary graph from the input graph, solve the problem on this smaller graph, and then use the solution to solve the original problem. We present a variant of this approach in which the smaller graph inherits the connectivity properties of the original graph. This is especially useful when trying to so...

A strict orthogonal drawing of a graph G = (V,E) in R is a drawing of G such that each vertex is mapped to a distinct point and each edge is mapped to a horizontal or vertical line segment. A graph G is HV -restricted if each of its edges is assigned a horizontal or vertical orientation. A strict orthogonal drawing of an HV -restricted graph G is good if it is planar and respects the edge orien...

Knowledge graph embedding represents entities and relations in knowledge graph as low-dimensional, continuous vectors, and thus enables knowledge graph compatible with machine learning models. Though there have been a variety of models for knowledge graph embedding, most methods merely concentrate on the fact triples, while supplementary textual descriptions of entities and relations have not b...

In this paper, we consider the problem of embedding a given graph into a fixed-size hypercube. This work is related to other recent research on hypercube embedding. In [1], Bhat describes an order IVl log2 IVI algorithm for testing whether a given graph G = (V, E) is exactly an n-cube. Deciding whether a graph has a distance-preserving embedding into a hypercube can be done in polynomial time [...

An L-segment consists of a horizontal and a vertical straight line which form an L. In an L-embedding of a graph, each vertex is represented by an Lsegment, and two segments intersect each other if and only if the corresponding vertices are adjacent in the graph. If the corner of each L-segment in an Lembedding lies on a straight line, we call it a monotone L-embedding. In this paper we give a ...

While the growing corpus of knowledge is now being encoded in the form of knowledge graphs with rich semantics, the current graph embedding models do not incorporate ontology information into themodeling.We propose a scalable and ontology-aware graph embedding model, EmbedS, which is able to capture RDFS ontological assertions. EmbedS models entities, classes, and properties differently in an R...

This paper investigates the problem of embedding planar graphs in books of few pages. An efficient algorithm for embedding a planar graph in a book establishes an upper bound of seven pages for any planar graph. This disproves a conjecture of Bernhart and Kainen that the pagenumber of a planar graph can be arbitrarily large. I t is also shown that the stellations of K3 have pagenumber three, th...

We consider the problem of simultaneous embedding of planar graphs. We demonstrate how to simultaneously embed a path and an n-level planar graph and how to use radial embeddings for curvilinear simultaneous embeddings of a path and an outerplanar graph. We also show how to use star-shaped levels to find 2-bends per path edge simultaneous embeddings of a path and an outerplanar graph. All embed...