Related papers: The Asymptotics of Quantum Max-Flow Min-Cut
We study error exponents for the problem of low-rate communication over a directed graph, where each edge in the graph represents a noisy communication channel, and there is a single source and destination. We derive maxflow-based…
We discuss how various models of scale-free complex networks approach their limiting properties when the size N of the network grows. We focus mainly on equilibrated networks and their finite-size degree distributions. Our results show that…
Structural and computational understanding of tensors is the driving force behind faster matrix multiplication algorithms, the unraveling of quantum entanglement, and the breakthrough on the cap set problem. Strassen's asymptotic spectra…
The problem of balancing covariates arises in observational studies where one is given a group of control samples and another group, disjoint from the control group, of treatment samples. Each sample, in either group, has several observed…
The Nisan-Ronen conjecture states that no truthful mechanism for makespan-minimization when allocating $m$ tasks to $n$ unrelated machines can have approximation ratio less than $n$. Over more than two decades since its formulation, little…
Physical and functional constraints on biological networks lead to complex topological patterns across multiple scales in their organization. A particular type of higher-order network feature that has received considerable interest is…
We prove three new lower bounds for graph connectivity in the $1$-bit broadcast congested clique model, BCC$(1)$. First, in the KT-$0$ version of BCC$(1)$, in which nodes are aware of neighbors only through port numbers, we show an…
In this work we prove convergence results of sequences of Riemannian $4$-manifolds with almost vanishing $L^2$-norm of a curvature tensor and a non-collapsing bound on the volume of small balls. In Theorem 1.1, we consider a sequence of…
In this article, we explicitly derive the limiting degree distribution of the shortest path tree from a single source on various random network models with edge weights. We determine the asymptotics of the degree distribution for large…
Random K-out graphs are used in several applications including modeling by sensor networks secured by the random pairwise key predistribution scheme, and payment channel networks. The random K-out graph with $n$ nodes is constructed as…
We show that every $\alpha$-approximate minimum cut in a connected graph is the unique minimum $(S,T)$-terminal cut for some subsets $S$ and $T$ of vertices each of size at most $\lfloor2\alpha\rfloor+1$. This leads to an alternative proof…
We study the problem of extracting a selective connector for a given set of query vertices $Q \subseteq V$ in a graph $G = (V,E)$. A selective connector is a subgraph of $G$ which exhibits some cohesiveness property, and contains the query…
We consider the problem of finding the value of a maximum flow over time in a network with uniform edge lengths where the edge capacities change at specific time instants. To solve this problem, we show how to construct a condensed version…
We investigate the space complexity of two graph streaming problems: Max-Cut and its quantum analogue, Quantum Max-Cut. Previous work by Kapralov and Krachun [STOC `19] resolved the classical complexity of the \emph{classical} problem,…
Network pruning is used to reduce inference latency and power consumption in large neural networks. However, most current pruning methods rely on ad-hoc heuristics that are poorly understood. We introduce Hyperflux, a conceptually-grounded…
We study first passage percolation on the configuration model. Assuming that each edge has an independent exponentially distributed edge weight, we derive explicit distributional asymptotics for the minimum weight between two randomly…
Manturov recently introduced the idea of a free knot, i.e. an equivalence class of virtual knots where equivalence is generated by crossing change and virtualization moves. He showed that if a free knot diagram is associated to a graph that…
In the decremental single-source shortest paths problem, the goal is to maintain distances from a fixed source $s$ to every vertex $v$ in an $m$-edge graph undergoing edge deletions. In this paper, we conclude a long line of research on…
We analyze a class of distributed quantized consen- sus algorithms for arbitrary networks. In the initial setting, each node in the network has an integer value. Nodes exchange their current estimate of the mean value in the network, and…
Numerous networks, such as transportation, distribution and delivery networks optimize their designs in order to increase efficiency and lower costs, improving the stability of its intended functions, etc. Networks that distribute goods,…