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This paper presents the design and analysis of a Hybrid High-Order (HHO) approximation for a distributed optimal control problem governed by the Poisson equation. We propose three distinct schemes to address unconstrained control problems…

Shannon's channel coding theorem describes the maximum possible rate of reliable information transfer through a classical noisy communication channel. It, together with the source coding theorem, characterizes lossless channel communication…

Scalable addressing of high dimensional constrained combinatorial optimization problems is a challenge that arises in several science and engineering disciplines. Recent work introduced novel application of graph neural networks for solving…

We give the first analysis of the computational complexity of {\it coalition structure generation over graphs}. Given an undirected graph $G=(N,E)$ and a valuation function $v:2^N\rightarrow\RR$ over the subsets of nodes, the problem is to…

We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving ERM problems with a nonsmooth regularization term. Current second-order and quasi-Newton methods for this…

We analyze the expressivity of a universal deep neural network that can be organized as a series of nested qubit rotations, accomplished by adjustable data re-uploads. While the maximal expressive power increases with the depth of the…

In this paper, we prove topology dependent bounds on the number of rounds needed to compute Functional Aggregate Queries (FAQs) studied by Abo Khamis et al. [PODS 2016] in a synchronous distributed network under the model considered by…

Recent Newton-type federated learning algorithms have demonstrated linear convergence with respect to the communication rounds. However, communicating Hessian matrices is often unfeasible due to their quadratic communication complexity. In…

Recently, many convolutional neural network (CNN) methods have been designed for hyperspectral image (HSI) classification since CNNs are able to produce good representations of data, which greatly benefits from a huge number of parameters.…

We propose an improved convergence analysis technique that characterizes the distributed learning paradigm of federated learning (FL) with imperfect/noisy uplink and downlink communications. Such imperfect communication scenarios arise in…

In coding theory, the problem of list recovery asks one to find all codewords $c$ of a given code $C$ which such that at least $1-\rho$ fraction of the symbols of $c$ lie in some predetermined set of $\ell$ symbols for each coordinate of…

This paper studies the problem of counting homomorphisms from a bipartite source graph to a bipartite target graph. An exact formula is first derived for the number of homomorphisms from a complete bipartite graph into a general bipartite…

In the {\sc Hitting Set} problem, we are given a collection $\cal F$ of subsets of a ground set $V$ and an integer $p$, and asked whether $V$ has a $p$-element subset that intersects each set in $\cal F$. We consider two parameterizations…

Combinatorial optimization problems are typically tackled by the branch-and-bound paradigm. We propose a new graph convolutional neural network model for learning branch-and-bound variable selection policies, which leverages the natural…

Due to the communication bottleneck in distributed and federated learning applications, algorithms using communication compression have attracted significant attention and are widely used in practice. Moreover, the huge number, high…

Computational intractability has for decades motivated the development of a plethora of methodologies that mainly aimed at a quality-time trade-off. The use of Machine Learning techniques has finally emerged as one of the possible tools to…

Tensor networks have been an important concept and technique in many research areas, such as quantum computation and machine learning. We study the exponential complexity of contracting tensor networks on two special graph structures:…

We improve the best known lower bounds on the exponential behavior of the maximum of the number of connected sets, $N(G)$, and dominating connected sets, $N_{dom}(G)$, for regular graphs. These lower bounds are improved by constructing a…

Graph Neural Networks (GNNs) have superior capability in learning graph data. Full-graph GNN training generally has high accuracy, however, it suffers from large peak memory usage and encounters the Out-of-Memory problem when handling large…

The notions of bounded expansion and nowhere denseness have been applied very successfully in algorithmic graph theory. We study the corresponding notions of directed bounded expansion and nowhere crownfulness on directed graphs. We show…