Related papers: E-Graphs With Bindings
This paper addresses the problem of synchronizing orthogonal matrices over directed graphs. For synchronized transformations (or matrices), composite transformations over loops equal the identity. We formulate the synchronization problem as…
A graph G is {\xi}-nearly planar if it can be embedded in the sphere so that each of its edges is crossed at most {\xi} times. The family of {\xi}-nearly planar graphs is widely extending the notion of planarity. We introduce an alternative…
New algorithms for embedding graphs have reduced the asymptotic complexity of finding low-dimensional representations. One-Hot Graph Encoder Embedding (GEE) uses a single, linear pass over edges and produces an embedding that converges…
Term graph rewriting provides a formalism for implementing term rewriting in an efficient manner by avoiding duplication. Infinitary term rewriting has been introduced to study infinite term reduction sequences. Such infinite reductions can…
We present a new and powerful algebraic framework for graph rewriting, based on drags, a class of graphs enjoying a novel composition operator. Graphs are embellished with roots and sprouts, which can be wired together to form edges. Drags…
The literature on word-representable graphs is quite rich, and a number of variations of the original definition have been proposed over the years. We are initiating a systematic study of such variations based on formal languages. In our…
Open-world semi-supervised learning aims at inferring both known and novel classes in unlabeled data, by harnessing prior knowledge from a labeled set with known classes. Despite its importance, there is a lack of theoretical foundations…
The continuous and rapid growth of highly interconnected datasets, which are both voluminous and complex, calls for the development of adequate processing and analytical techniques. One method for condensing and simplifying such datasets is…
Graphs can be used to represent a wide variety of data belonging to different domains. Graphs can capture the relationship among data in an efficient way, and have been widely used. In recent times, with the advent of Big Data, there has…
While advances in computing resources have made processing enormous amounts of data possible, human ability to identify patterns in such data has not scaled accordingly. Efficient computational methods for condensing and simplifying data…
We address the problem of reasoning on graph transformations featuring actions such as \emph{addition} and \emph{deletion} of nodes and edges, node \emph{merging} and \emph{cloning}, node or edge \emph{labelling} and edge…
Automated construction of bilingual dictionaries using monolingual embedding spaces is a core challenge in machine translation. The end performance of these dictionaries relies upon the geometric similarity of individual spaces, i.e., their…
Graph-based semantic representations are valuable in natural language processing, where it is often simple and effective to represent linguistic concepts as nodes, and relations as edges between them. Several attempts has been made to find…
Adjacency between two vertices in graphs or hypergraphs is a pairwise relationship. It is redefined in this article as 2-adjacency. In general hypergraphs, hyperedges hold for $n$-adic relationship. To keep the $n$-adic relationship the…
Graph is a natural representation of data for a variety of real-word applications, such as knowledge graph mining, social network analysis and biological network comparison. For these applications, graph embedding is crucial as it provides…
The correspondence between monoidal categories and graphical languages of diagrams has been studied extensively, leading to applications in quantum computing and communication, systems theory, circuit design and more. From the categorical…
The Homeomorphic Embedding relation has been amply used for defining termination criteria of symbolic methods for program analysis, transformation, and verification. However, homeomorphic embedding has never been investigated in the context…
Graph alignment aims at finding the vertex correspondence between two correlated graphs, a task that frequently occurs in graph mining applications such as social network analysis. Attributed graph alignment is a variant of graph alignment,…
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…
The basic principle of graph rewriting is the stepwise replacement of subgraphs inside a host graph. A challenge in such replacement steps is the treatment of the patch graph, consisting of those edges of the host graph that touch the…