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Graph Retrieval has witnessed continued interest and progress in the past few years. In thisreport, we focus on neural network based approaches for Graph matching and retrieving similargraphs from a corpus of graphs. We explore methods…
We prove that the ribbon graph polynomial of a graph embedded in an orientable surface is irreducible if and only if the embedded graph is neither the disjoint union nor the join of embedded graphs. This result is analogous to the fact that…
Graphs face challenges when dealing with massive datasets. They are essential tools for modeling interconnected data and often become computationally expensive. Graph embedding techniques, on the other hand, provide an efficient approach.…
Aligning a sequence to a walk in a labeled graph is a problem of fundamental importance to Computational Biology. For finding a walk in an arbitrary graph with $|E|$ edges that exactly matches a pattern of length $m$, a lower bound based on…
We propose an efficient algorithm for matching two correlated Erd\H{o}s--R\'enyi graphs with $n$ vertices whose edges are correlated through a latent vertex correspondence. When the edge density $q= n^{- \alpha+o(1)}$ for a constant $\alpha…
Two graphs $G_1=(V,E_1)$ and $G_2=(V,E_2)$ admit a geometric simultaneous embedding if there exists a set of points P and a bijection M: P -> V that induce planar straight-line embeddings both for $G_1$ and for $G_2$. While it is known that…
There is a well-known way to describe a link diagram as a (signed) plane graph, called its Tait graph. This concept was recently extended, providing a way to associate a set of embedded graphs (or ribbon graphs) to a link diagram. While…
Graph similarity computation is one of the core operations in many graph-based applications, such as graph similarity search, graph database analysis, graph clustering, etc. Since computing the exact distance/similarity between two graphs…
Partial duality generalizes the fundamental concept of the geometric dual of an embedded graph. A partial dual is obtained by forming the geometric dual with respect to only a subset of edges. While geometric duality preserves the genus of…
Graph embedding maps graph nodes to low-dimensional vectors, and is widely adopted in machine learning tasks. The increasing availability of billion-edge graphs underscores the importance of learning efficient and effective embeddings on…
Matching landmark patches from a real-time image captured by an on-vehicle camera with landmark patches in an image database plays an important role in various computer perception tasks for autonomous driving. Current methods focus on local…
Large graphs are difficult to represent, visualize, and understand. In this paper, we introduce "gate graph" - a new approach to perform graph simplification. A gate graph provides a simplified topological view of the original graph.…
This work studies certain aspects of graphs embedded on surfaces. Initially, a colored graph model for a map of a graph on a surface is developed. Then, a concept analogous to (and extending) planar graph is introduced in the same spirit as…
Graph-based approaches are empirically shown to be very successful for the nearest neighbor search (NNS). However, there has been very little research on their theoretical guarantees. We fill this gap and rigorously analyze the performance…
We describe a data structure, a rectangular complex, that can be used to represent hyperconvex metric spaces that have the same topology (although not necessarily the same distance function) as subsets of the plane. We show how to use this…
We demonstrate that a graph-based search algorithm-relying on the construction of an approximate neighborhood graph-can directly work with challenging non-metric and/or non-symmetric distances without resorting to metric-space mapping…
The random graph is an infinite graph with the universal property that any embedding of $G-v$ extends to an embedding of $G$, for any finite graph. In this paper we show that this graph embeds in the curve graph of a surface $\Sigma$ if and…
Embedding static graphs in low-dimensional vector spaces plays a key role in network analytics and inference, supporting applications like node classification, link prediction, and graph visualization. However, many real-world networks…
Optimization-based methods are commonly applied in autonomous driving trajectory planners, which transform the continuous-time trajectory planning problem into a finite nonlinear program with constraints imposed at finite collocation…
The problem of finding a marked node in a graph can be solved by the spatial search algorithm based on continuous-time quantum walks (CTQW). However, this algorithm is known to run in optimal time only for a handful of graphs. In this work,…