Related papers: Random Subnetworks of Random Sorting Networks
The recent lottery ticket hypothesis proposes that there is one sub-network that matches the accuracy of the original network when trained in isolation. We show that instead each network contains several winning tickets, even if the initial…
A very popular class of models for networks posits that each node is represented by a point in a continuous latent space, and that the probability of an edge between nodes is a decreasing function of the distance between them in this latent…
Consider a graph G with n nodes and m edges, which represents a social network, and assume that initially each node is blue or white. In each round, all nodes simultaneously update their color to the most frequent color in their…
In this work, we formulate and study a data dissemination problem, which can be viewed as a generalization of the index coding problem and of the data exchange problem to networks with an arbitrary topology. We define $r$-solvable networks,…
For any pair of integers $m$ and $n$ such that $3<m<n$, we provide an infinite family of links, where each link in the family has a locally minimal $n$-bridge position and a globally minimal $m$-bridge position. We accomplish this by…
Multi-layered social networks consist of the fixed set of nodes linked by multiple connections. These connections may be derived from different types of user activities logged in the IT system. To calculate any structural measures for…
We discuss two sampling schemes for selecting random subnets from a network: Random sampling and connectivity dependent sampling, and investigate how the degree distribution of a node in the network is affected by the two types of sampling.…
We develop a new algorithmic technique that allows to transfer some constant time approximation algorithms for general graphs into random order streaming algorithms. We illustrate our technique by proving that in random order streams with…
In the present paper, we derive an upper bound of the average network breakdown probability of packet networks with unreliable relay nodes. We here assume that relay nodes get independently broken with a given node breakdown probability. A…
This paper presents an algorithm for searching for the minimum number of neurons in fully connected layers of an arbitrary network solving given problem, which does not require multiple training of the network with different number of…
In designing a network to link n cities in a square of area n, one might be guided by the following two desiderata. First, the total network length should not be much greater than the length of the shortest network connecting all cities.…
Random tensor networks are a powerful toy model for understanding the entanglement structure of holographic quantum gravity. However, unlike holographic quantum gravity, their entanglement spectra are flat. It has therefore been argued that…
One model of message delivery in a computer network is based on labelling each edge by a subset of a (reasonably small) universal set, and then encoding a path as the union of the labels of its edges. Earlier work suggested using random…
Let G=(V,E) be an undirected loopless graph with possible parallel edges and s and t be two vertices of G. Assume that vertex s is labelled at the initial time step and that every labelled vertex copies its labelling to neighbouring…
Given a rooted tree and a ranking of its leaves, what is the minimum number of inversions of the leaves that can be attained by ordering the tree? This variation of the problem of counting inversions in arrays originated in mathematical…
This paper considers the \textit{minimum spanning tree (MST)} problem in the Congested Clique model and presents an algorithm that runs in $O(\log \log \log n)$ rounds, with high probability. Prior to this, the fastest MST algorithm in this…
The seeded Watershed algorithm / minimax semi-supervised learning on a graph computes a minimum spanning forest which connects every pixel / unlabeled node to a seed / labeled node. We propose instead to consider all possible spanning…
Merging-based sorting networks are an important family of sorting networks. Most merge sorting networks are based on 2-way or multi-way merging algorithms using 2-sorters as basic building blocks. An alternative is to use n-sorters, instead…
In this paper we present a random shuffling scheme to apply with adaptive sorting algorithms. Adaptive sorting algorithms utilize the presortedness present in a given sequence. We have probabilistically increased the amount of presortedness…
A random geometric digraph $G_n$ is constructed by taking $\{X_1,X_2,... X_n\}$ in $\mathbb{R}^2$ independently at random with a common bounded density function. Each vertex $X_i$ is assigned at random a sector $S_i$ of central angle…