Related papers: A Graph Minor Perspective to Multicast Network Cod…

Robertson and Seymour's celebrated Graph Minor Theorem states that graphs are well-quasi-ordered by the minor relation. Unlike the minor relation, the topological minor relation does not well-quasi-order graphs in general. Among all known…

We consider a network coding setting where some of the messages and edges have fixed alphabet sizes, that do not change when we increase the common alphabet size of the rest of the messages and edges. We prove that the problem of deciding…

This paper looks at the task of network topology inference, where the goal is to learn an unknown graph from nodal observations. One of the novelties of the approach put forth is the consideration of prior information about the density of…

Network coding (NC), in principle, is a Layer-3 innovation that improves network throughput in wired networks for multicast/broadcast scenarios. Due to the fundamental differences between wired and wireless networks, extending NC to…

Due to the advent of the expressions of data other than tabular formats, the topological compositions which make samples interrelated came into prominence. Analogically, those networks can be interpreted as social connections, dataflow…

In this work, we study the problem of index coding from graph homomorphism perspective. We show that the minimum broadcast rate of an index coding problem for different variations of the problem such as non-linear, scalar, and vector index…

Many protocols of quantum information processing, like quantum key distribution or measurement-based quantum computation, "consume" entangled quantum states during their execution. When participants are located at distant sites, these…

In this short paper, a neural network that is able to form a low dimensional topological hidden representation is explained. The neural network can be trained as an autoencoder, a classifier or mix of both, and produces different low…

Network detection is an important capability in many areas of applied research in which data can be represented as a graph of entities and relationships. Oftentimes the object of interest is a relatively small subgraph in an enormous,…

In traditional Graph Neural Networks (GNN), graph convolutional learning is carried out through topology-driven recursive node content aggregation for network representation learning. In reality, network topology and node content are not…

We investigate Hadwiger's conjecture for graphs with no stable set of size 3. Such a graph on at least 2t-1 vertices is not t-1 colorable, so is conjectured to have a $K_t$ minor. There is a strengthening of Hadwiger's conjecture in this…

An identifying code of a graph is a dominating set which uniquely determines all the vertices by their neighborhood within the code. Whereas graphs with large minimum degree have small domination number, this is not the case for the…

The sorting number of a graph with $n$ vertices is the minimum depth of a sorting network with $n$ inputs and outputs that uses only the edges of the graph to perform comparisons. Many known results on sorting networks can be stated in…

A mathematical topology with matrix is a natural representation of a coding relational structure that is found in many fields of the world. Matrices are very important in computation of real applications, s ce matrices are easy saved in…

This paper considers quantum network coding, which is a recent technique that enables quantum information to be sent on complex networks at higher rates than by using straightforward routing strategies. Kobayashi et al. have recently showed…

Geometry can be used to explain many properties commonly observed in real networks. It is therefore often assumed that real networks, especially those with high average local clustering, live in an underlying hidden geometric space.…

A fundamental result in structural graph theory states that every graph with large average degree contains a large complete graph as a minor. We prove this result with the extra property that the minor is small with respect to the order of…

A network can be analyzed at different topological scales, ranging from single nodes to motifs, communities, up to the complete structure. We propose a novel intermediate-level topological analysis that considers non-overlapping subgraphs…

Network topology inference is a cornerstone problem in statistical analyses of complex systems. In this context, the fresh look advocated here permeates benefits from convex optimization and graph signal processing, to identify the…

We consider the problem of minimizing the number of broadcasts for collecting all sensor measurements at a sink node in a noisy broadcast sensor network. Focusing first on arbitrary network topologies, we provide (i) fundamental limits on…