Related papers: Mathematical Foundations for Peer-to-Peer Lattice …
We introduce a new, "worst-case" model for an asynchronous communication network and investigate the simplest (yet central) task in this model, namely the feasibility of end-to-end routing. Motivated by the question of how successful a…
The Sparsest Cut is a fundamental optimization problem that has been extensively studied. For planar inputs the problem is in $P$ and can be solved in $\tilde{O}(n^3)$ time if all vertex weights are $1$. Despite a significant amount of…
We consider Markov models of large-scale networks where nodes are characterized by their local behavior and by a mobility model over a two-dimensional lattice. By assuming random walk, we prove convergence to a system of partial…
Upper bounds on the communication complexity of finding the nearest lattice point in a given lattice $\Lambda \subset \mathbb{R}^2$ was considered in earlier works~\cite{VB:2017}, for a two party, interactive communication model. Here we…
The space-requirement for routing-tables is an important characteristic of routing schemes. For the cost-measure of minimizing the total network load there exist a variety of results that show tradeoffs between stretch and required size for…
Federated learning must address heterogeneity, strict communication and computation limits, and privacy while ensuring performance. We propose an operator-theoretic framework that maps the $L^2$-optimal solution into a reproducing kernel…
We implement and test the performances of several approximation algorithms for computing the minimum dominating set of a graph. These algorithms are the standard greedy algorithm, the recent LP rounding algorithms and a hybrid algorithm…
Two-stage methods addressing continuous shortest path problems start local minimization from discrete shortest paths in a spatial graph. The convergence of such hybrid methods to global minimizers hinges on the discretization error induced…
We investigate problems addressing combined connectivity augmentation and orientations settings. We give a polynomial-time 6-approximation algorithm for finding a minimum cost subgraph of an undirected graph $G$ that admits an orientation…
The $sl(2)$ minimal theories are labelled by a Lie algebra pair $(A,G)$ where $G$ is of $A$-$D$-$E$ type. For these theories on a cylinder we conjecture a complete set of conformal boundary conditions labelled by the nodes of the tensor…
In a capacitated directed graph, it is known that the set of all min-cuts forms a distributive lattice [1], [2]. Here, we describe this lattice as a regular predicate whose forbidden elements can be advanced in constant parallel time after…
We study a spatiotemporal service matching problem in which demand, heterogeneous in location and time sensitivity/preference, is to be assigned to service stations. The planner seeks to maximize social welfare, defined as total service…
In the problem of minimum connected dominating set with routing cost constraint, we are given a graph $G=(V,E)$, and the goal is to find the smallest connected dominating set $D$ of $G$ such that, for any two non-adjacent vertices $u$ and…
Being able to provide latency guarantees for orbital edge computing applications through Low Earth Orbit (LEO) satellite constellations is a major milestone for their integration into 5G and 6G networks. However, achieving this is…
By offloading intensive computation tasks to the edge cloud located at the cellular base stations, mobile-edge computation offloading (MECO) has been regarded as a promising means to accomplish the ambitious millisecond-scale end-to-end…
We pursue a study of the Generalized Demand Matching problem, a common generalization of the $b$-Matching and Knapsack problems. Here, we are given a graph with vertex capacities, edge profits, and asymmetric demands on the edges. The goal…
We propose in this article an adaptation of the basic techniques of the deterministic network calculus theory to the road traffic flow theory. Network calculus is a theory based on min-plus algebra. It uses algebraic techniques to compute…
Interconnection networks provide an effective mechanism for exchanging data between processors in a parallel computing system. One of the most efficient interconnection networks is the hypercube due to its structural regularity, potential…
Defect-adaptive surface-code methods have substantially advanced the construction of valid logical patches on imperfect hardware, but fault-tolerant computation also requires executable logical oper ations on the resulting irregular…
We propose a new model for peer-to-peer networking which takes the network bottlenecks into account beyond the access. This model allows one to cope with key features of P2P networking like degree or locality constraints or the fact that…