Related papers: Embeddings into the Pancake Interconnection Networ…
One of the important features of an interconnection network is its ability to efficiently simulate programs or parallel algorithms written for other architectures. Such a simulation problem can be mathematically formulated as a graph…
High parallel framework has been proved to be very suitable for graph processing. There are various work to optimize the implementation in FPGAs, a pipeline parallel device. The key to make use of the parallel performance of FPGAs is to…
We study the classic problem of fairly dividing a heterogeneous and divisible resource -- represented by a cake, $[0,1]$ -- among $n$ agents. This work considers an interesting variant of the problem where agents are embedded on a graph.…
Traditional representations of graphs and their duals suggest the requirement that the dual vertices be placed inside their corresponding primal faces, and the edges of the dual graph cross only their corresponding primal edges. We consider…
We prove that circle graphs (intersection graphs of circle chords) can be embedded as intersection graphs of rays in the plane with polynomial-size bit complexity. We use this embedding to show that the global curve simplification problem…
Learning graph representations via low-dimensional embeddings that preserve relevant network properties is an important class of problems in machine learning. We here present a novel method to embed directed acyclic graphs. Following prior…
Torus networks of moderate degree have been widely used in the supercomputer industry. Tori are superb when used for executing applications that require near-neighbor communications. Nevertheless, they are not so good when dealing with…
Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of…
Stable topological invariants are a cornerstone of persistence theory and applied topology, but their discriminative properties are often poorly-understood. In this paper we study a rich homology-based invariant first defined by Dey, Shi,…
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.…
Mapping complex input data into suitable lower dimensional manifolds is a common procedure in machine learning. This step is beneficial mainly for two reasons: (1) it reduces the data dimensionality and (2) it provides a new data…
Superpixels are a useful representation to reduce the complexity of image data. However, to combine superpixels with convolutional neural networks (CNNs) in an end-to-end fashion, one requires extra models to generate superpixels and…
We develop a novel parallel decomposition strategy for unweighted, undirected graphs, based on growing disjoint connected clusters from batches of centers progressively selected from yet uncovered nodes. With respect to similar previous…
Distributed computing has become a common practice nowadays, where the recent focus has been given to the usage of smart networking devices with in-network computing capabilities. State-of-the-art switches with near-line rate computing and…
A rectangle in the plane can be continuously deformed preserving its edge lengths, but adding a diagonal brace prevents such a deformation. Bolker and Crapo characterized combinatorially which choices of braces make a grid of squares…
Graph is a ubiquitous representation of data in various research fields, and graph embedding is a prevalent machine learning technique for capturing key features and generating fixed-sized attributes. However, most state-of-the-art graph…
Extending Stallings' foldings of trees, we show in this article that every parallel-preserving map between median graphs factors as an isometric embedding through a sequence of elementary transformations which we call foldings and…
We tackle the problem of graph partitioning for image segmentation using correlation clustering (CC), which we treat as an integer linear program (ILP). We reformulate optimization in the ILP so as to admit efficient optimization via…
Node embeddings map graph vertices into low-dimensional Euclidean spaces while preserving structural information. They are central to tasks such as node classification, link prediction, and signal reconstruction. A key goal is to design…
The convolution operator at the core of many modern neural architectures can effectively be seen as performing a dot product between an input matrix and a filter. While this is readily applicable to data such as images, which can be…