Related papers: Inserting an Edge into a Geometric Embedding
The Bandwidth Theorem of B\"ottcher, Schacht and Taraz [Mathematische Annalen 343 (1), 175-205] gives minimum degree conditions for the containment of spanning graphs H with small bandwidth and bounded maximum degree. We generalise this…
Graph neural networks (GNNs) are the dominant approach to solving machine learning problems defined over graphs. Despite much theoretical and empirical work in recent years, our understanding of finer-grained aspects of architectural design…
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The basic (and traditional) crossing number problem is to determine the minimum number of crossings in a topological drawing of an input graph in the plane. We develop a unified framework yielding fixed-parameter tractable (FPT) algorithms…
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One of the most important combinatorial optimization problems is graph coloring. There are several variations of this problem involving additional constraints either on vertices or edges. They constitute models for real applications, such…
A set of colored graphs are compatible, if for every color $i$, the number of vertices of color $i$ is the same in every graph. A simultaneous embedding of $k$ compatibly colored graphs, each with $n$ vertices, consists of $k$ planar…
In the subgraph counting problem, we are given a input graph $G(V, E)$ and a target graph $H$; the goal is to estimate the number of occurrences of $H$ in $G$. Our focus here is on designing sublinear-time algorithms for approximately…
A number of computations exist, especially in area of error-control coding and matrix computations, whose underlying data flow graphs are based on finite projective-geometry(PG) based balanced bipartite graphs. Many of these applications…
The crossing angle of a straight-line drawing $\Gamma$ of a graph $G=(V, E)$ is the smallest angle between two crossing edges in $\Gamma$. Deciding whether a graph $G$ has a straight-line drawing with a crossing angle of $90^\circ$ is…
Graph embedding provides an efficient solution for graph analysis by converting the graph into a low-dimensional space which preserves the structure information. In contrast to the graph structure data, the i.i.d. node embedding can be…
Recently, one has seen a surge of interest in developing such methods including ones for learning such representations for (undirected) graphs (while preserving important properties). However, most of the work to date on embedding graphs…
An edge-weighted graph $G=(V,E)$ is called stable if the value of a maximum-weight matching equals the value of a maximum-weight fractional matching. Stable graphs play an important role in some interesting game theory problems, such as…
Learning low-dimensional numerical representations from symbolic data, e.g., embedding the nodes of a graph into a geometric space, is an important concept in machine learning. While embedding into Euclidean space is common, recent…
De Berg et al. in [SICOMP 2020] gave an algorithmic framework for subexponential algorithms on geometric graphs with tight (up to ETH) running times. This framework is based on dynamic programming on graphs of weighted treewidth resulting…
A graph embedding algorithm embeds a graph into a low-dimensional space such that the embedding preserves the inherent properties of the graph. While graph embedding is fundamentally related to graph visualization, prior work did not…
We initiate the study of a fundamental combinatorial problem: Given a capacitated graph $G=(V,E)$, find a shortest walk ("route") from a source $s\in V$ to a destination $t\in V$ that includes all vertices specified by a set…
Graph matching refers to finding node correspondence between graphs, such that the corresponding node and edge's affinity can be maximized. In addition with its NP-completeness nature, another important challenge is effective modeling of…