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We study principal component analysis (PCA), where given a dataset in $\mathbb{R}^d$ from a distribution, the task is to find a unit vector $v$ that approximately maximizes the variance of the distribution after being projected along $v$.…
Optimal linear-time algorithms for testing the planarity of a graph are well-known for over 35 years. However, these algorithms are quite involved and recent publications still try to give simpler linear-time tests. We give a simple…
We study the single pair capacitated network design problem and the budget constrained max flow problem on undirected series-parallel graphs. These problems were well studied on directed series-parallel graphs, but little is known in the…
The connections in many networks are not merely binary entities, either present or not, but have associated weights that record their strengths relative to one another. Recent studies of networks have, by and large, steered clear of such…
We prove the existence of the flow by curvature of regular planar networks starting from an initial network which is non-regular. The proof relies on a monotonicity formula for expanding solutions and a local regularity result for the…
In the Flow Edge-Monitor Problem, we are given an undirected graph G=(V,E), an integer k > 0 and some unknown circulation \psi on G. We want to find a set of k edges in G, so that if we place k monitors on those edges to measure the flow…
Due to the non-stationarity of time series, the distribution shift problem largely hinders the performance of time series forecasting. Existing solutions either rely on using certain statistics to specify the shift, or developing specific…
In numerical linear algebra, considerable effort has been devoted to obtaining faster algorithms for linear systems whose underlying matrices exhibit structural properties. A prominent success story is the method of generalized nested…
While numerous forecasters have been proposed using different network architectures, the Transformer-based models have state-of-the-art performance in time series forecasting. However, forecasters based on Transformers are still suffering…
A type assignment system for lambda-calculus enjoys the principal typing property if every typable term M has a special typing, called principal, from which all typings for M can be obtained via suitable operations. The existence of…
Network traffic monitoring using IP flows is used to handle the current challenge of analyzing encrypted network communication. Nevertheless, the packet aggregation into flow records naturally causes information loss; therefore, this paper…
We consider the problem of network coding across multiple unicasts. We give, for wired and wireless networks, efficient polynomial time algorithms for finding optimal network codes within the class of network codes restricted to XOR coding…
We introduce an algorithmic framework based on tensor networks for computing fluid flows around immersed objects in curvilinear coordinates. We show that the tensor network simulations can be carried out solely using highly compressed…
We introduce Forman-Ricci curvature and its corresponding flow as characteristics for complex networks attempting to extend the common approach of node-based network analysis by edge-based characteristics. Following a theoretical…
We propose a learning-augmented framework for accelerating max-flow computation and image segmentation by integrating Graph Neural Networks (GNNs) with the Ford-Fulkerson algorithm. Rather than predicting initial flows, our method learns…
Hierarchical structure and repetition are prevalent in graphs originating from nature or engineering. These patterns can be represented by a class of parametric-structure graphs, which are defined by templates that generate structure by way…
Traffic prediction is a fundamental and vital task in Intelligence Transportation System (ITS), but it is very challenging to get high accuracy while containing low computational complexity due to the spatiotemporal characteristics of…
Vertex connectivity and edge connectivity are fundamental concepts in graph theory that have been widely studied from both structural and algorithmic perspectives. The focus of this paper is on computing these two parameters for graphs…
The diameter of a graph is among its most basic parameters. Since a few years, it moreover became a key issue to compute it for massive graphs in the context of complex network analysis. However, known algorithms, including the ones…
In the last few years the so--called "linear deterministic" model of relay channels has gained popularity as a means of studying the flow of information over wireless communication networks, and this approach generalizes the model of…