Related papers: Interchanging distance and capacity in probabilist…
Many applications rely on time-intensive matrix operations, such as factorization, which can be sped up significantly for large sparse matrices by interpreting the matrix as a sparse graph and computing a node ordering that minimizes the…
To account for the randomness of propagation channels and interference levels in hierarchical spectrum sharing, a novel approach to multihop routing is introduced for cognitive random access networks, whereby packets are randomly routed…
We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…
This paper presents a matching mechanism for assigning drivers to routes where the drivers pay a toll for the marginal delay they impose on other drivers. The simple matching mechanism is derived from the RANKING algorithm for online…
The neighbourhood matrix, $\mathcal{NM}(G)$, a novel representation of graphs proposed in \cite {ALPaper} is defined using the neighbourhood sets of the vertices. The matrix also exhibits a bijection between the product of two well-known…
We present an analysis of the topologies of a class of networks which are optimal in terms of the requirements of having as short a route as possible between any two nodes while yet keeping the congestion in the network as low as possible.…
Imagine that unlabelled tokens are placed on the edges of a graph, such that no two tokens are placed on incident edges. A token can jump to another edge if the edges having tokens remain independent. We study the problem of determining the…
Directed graphs provide more subtle and precise modelling tools for optimization in road networks than simple graphs. In particular, they are more suitable in the context of alternative fuel vehicles and new automotive technologies, like…
Mobile-edge computing (MEC) has emerged as a prominent technique to provide mobile services with high computation requirement, by migrating the computation-intensive tasks from the mobile devices to the nearby MEC servers. To reduce the…
The use of complex networks as a modern approach to understanding the world and its dynamics is well-established in literature. The adjacency matrix, which provides a one-to-one representation of a complex network, can also yield several…
We present an optimal and efficient algorithm for finding a shortest path in an elastic optical network. The algorithm is an adaptation of the Dijkstra shortest path algorithm, where we take into account the spectrum continuity and…
In this work, we establish theoretical and practical connections between vertex indexing for sparse graph/network compression and matrix ordering for sparse matrix-vector multiplication and variable elimination. We present a fundamental…
A graph homomorphism is a map between two graphs that preserves adjacency relations. We consider the problem of sampling a random graph homomorphism from a graph into a large network. We propose two complementary MCMC algorithms for…
Properties of networks are often characterized in terms of features such as node degree distributions, average path lengths, diameters, or clustering coefficients. Here, we study shortest path length distributions. On the one hand, average…
For the task of moving a group of indistinguishable agents on a connected graph with unit edge lengths into an arbitrary goal formation, it was previously shown that distance optimal paths can be scheduled to complete with a tight…
Recent work has introduced sparse exchangeable graphs and the associated graphex framework, as a generalization of dense exchangeable graphs and the associated graphon framework. The development of this subject involves the interplay…
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…
The Thorup-Zwick (TZ) routing scheme is the first generic stretch-3 routing scheme delivering a nearly optimal local memory upper bound. Using both direct analysis and simulation, we calculate the stretch distribution of this routing scheme…
A simple and accurate relationship is demonstrated that links the average shortest path, nodes, and edges in a complex network. This relationship takes advantage of the concept of link density and shows a large improvement in fitting…
We present a comparative study of the application of a recently introduced heuristic algorithm to the optimization of transport on three major types of complex networks. The algorithm balances network traffic iteratively by minimizing the…