Related papers: Fast and Compact Planar Embeddings

The merging of succinct data structures is a well established technique for the space efficient construction of large succinct indexes. In the first part of the paper we propose a new algorithm for merging succinct representations of de…

We show how to preprocess a weighted undirected $n$-vertex planar graph in $\tilde O(n^{4/3})$ time, such that the distance between any pair of vertices can then be reported in $\tilde O(1)$ time. This improves the previous $\tilde…

Graph pattern matching is a fundamental problem encountered by many common graph mining tasks and the basic building block of several graph mining systems. This paper explores for the first time how to proactively prune graphs to speed up…

Let $G$ be a planar $3$-graph (i.e., a planar graph with vertex degree at most three) with $n$ vertices. We present the first $O(n^2)$-time algorithm that computes a planar orthogonal drawing of $G$ with the minimum number of bends in the…

Domain-specific languages that execute image processing pipelineson GPUs, such as Halide and Forma, operate by 1) dividing the image into overlapped tiles, and 2) fusing loops to improve memory locality. However, current approaches have…

Rigid frameworks in some Euclidian space are embedded graphs having a unique local realization (up to Euclidian motions) for the given edge lengths, although globally they may have several. We study the number of distinct planar embeddings…

Deep Neural Networks have impressive classification performance, but this comes at the expense of significant computational resources at inference time. Autonomous Underwater Vehicles use low-power embedded systems for sonar image…

In a general graph data structure like an adjacency matrix, when edges are homogeneous, the connectivity of two nodes can be sufficiently represented using a single bit. This insight has, however, not yet been adequately exploited by the…

We present an explicit and efficient construction of additively weighted Voronoi diagrams on planar graphs. Let $G$ be a planar graph with $n$ vertices and $b$ sites that lie on a constant number of faces. We show how to preprocess $G$ in…

A graph embedding is a representation of graph vertices in a low-dimensional space, which approximately preserves properties such as distances between nodes. Vertex sequence-based embedding procedures use features extracted from linear…

Graph neural networks (GNNs) start to gain momentum after showing significant performance improvement in a variety of domains including molecular science, recommendation, and transportation. Turning such performance improvement of GNNs into…

In the constrained planarity setting, we ask whether a graph admits a planar drawing that additionally satisfies a given set of constraints. These constraints are often derived from very natural problems; prominent examples are Level…

Graph Neural Networks (GNNs) are powerful deep learning models to generate node embeddings on graphs. When applying deep GNNs on large graphs, it is still challenging to perform training in an efficient and scalable way. We propose a novel…

Learning continuous representations of nodes is attracting growing interest in both academia and industry recently, due to their simplicity and effectiveness in a variety of applications. Most of existing node embedding algorithms and…

Designing efficient neural networks for embedded devices is a critical challenge, particularly in applications requiring real-time performance, such as aerial imaging with drones and UAVs for emergency responses. In this work, we introduce…

Clique and near-clique counts are important graph properties with applications in graph generation, graph modeling, graph analytics, community detection among others. They are the archetypal examples of dense subgraphs. While there are…

We describe an efficient new algorithm for the generation of fullerenes. Our implementation of this algorithm is more than 3.5 times faster than the previously fastest generator for fullerenes -- fullgen -- and the first program since…

We present space-efficient algorithms for computing cut vertices in a given graph with $n$ vertices and $m$ edges in linear time using $O(n+\min\{m,n\log \log n\})$ bits. With the same time and using $O(n+m)$ bits, we can compute the…

Merge trees are a valuable tool in the scientific visualization of scalar fields; however, current methods for merge tree comparisons are computationally expensive, primarily due to the exhaustive matching between tree nodes. To address…

Let $T$ be a string of length $n$ over an integer alphabet of size $\sigma$. In the word RAM model, $T$ can be represented in $O(n /\log_\sigma n)$ space. We show that a representation of all covers of $T$ can be computed in the optimal…