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Finding the dense regions of a graph and relations among them is a fundamental problem in network analysis. Core and truss decompositions reveal dense subgraphs with hierarchical relations. The incremental nature of algorithms for computing…
We introduce a new numerical method based on machine learning to approximate the solution of elliptic partial differential equations with collocation using a set of sigmoidal functions. We show that a feedforward neural network with a…
We study the complexity of fundamental distributed graph problems in the recently popular setting where information about the input graph is available to the nodes before the start of the computation. We focus on the most common such…
We propose a general method for converting online algorithms to local computation algorithms by selecting a random permutation of the input, and simulating running the online algorithm. We bound the number of steps of the algorithm using a…
We describe approximation algorithms in Linial's classic LOCAL model of distributed computing to find maximum-weight matchings in a hypergraph of rank $r$. Our main result is a deterministic algorithm to generate a matching which is an…
Biological and cellular systems are often modeled as graphs in which vertices represent objects of interest (genes, proteins, drugs) and edges represent relational ties among these objects (binds-to, interacts-with, regulates). This…
In the present paper, we study a multipoint boundary value problem for a system of Fredholm integro-differenial equations by the method of parameterization. The case of a degenerate kernel is studied separately, for which we obtain…
Online topology estimation of graph-connected time series is challenging, especially since the causal dependencies in many real-world networks are nonlinear. In this paper, we propose a kernel-based algorithm for graph topology estimation.…
This paper studies approximate solutions of a linear fractional vector optimization problem without requiring boundedness of the constraint set. We establish necessary and sufficient conditions for approximating weakly efficient points of…
We present a model for nonlocal diffusion with Neumann boundary conditions in a bounded smooth domain prescribing the flux through the boundary. We study the limit of this family of nonlocal diffusion operators when a rescaling parameter…
The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…
We design improved approximation algorithms for NP-hard graph problems by incorporating predictions (e.g., learned from past data). Our prediction model builds upon and extends the $\varepsilon$-prediction framework by Cohen-Addad, d'Orsi,…
In this paper, we present a fast and accurate numerical scheme for the solution of fifth-order boundary-value problems. We apply the reproducing kernel Hilbert space method (RKHSM) for solving this problem. The analytic results of the…
A dynamic graph algorithm is a data structure that supports edge insertions, deletions, and specific problem queries. While extensive research exists on dynamic algorithms for graph problems solvable in polynomial time, most of these…
We propose a new localized inference algorithm for answering marginalization queries in large graphical models with the correlation decay property. Given a query variable and a large graphical model, we define a much smaller model in a…
The combinatorial optimization problem is one of the important applications in neural network computation. The solutions of linearly constrained continuous optimization problems are difficult with an exact algorithm, but the algorithm for…
An algorithm is proposed to implement unsteady jump boundary conditions, presenting discontinuity in physical quantities, within the lattice Boltzmann method (LBM). This is useful to tackle problems involving mass or heat transfer through…
Overdetermined systems of first kind integral equations appear in many applications. When the right-hand side is discretized, the resulting finite-data problem is ill-posed and admits infinitely many solutions. We propose a numerical method…
The problem of solving linear systems is one of the most fundamental problems in computer science, where given a satisfiable linear system $(A,b)$, for $A \in \mathbb{R}^{n \times n}$ and $b \in \mathbb{R}^n$, we wish to find a vector $x…
As a main result of the paper, we construct and justify an asymptotic approximation of Green's function in a domain with many small inclusions. Periodicity of the array of inclusions is not required. We start with an analysis of the…