Related papers: Compact Routing on Internet-Like Graphs
For a random walk on a network, the mean first-passage time from a node $i$ to another node $j$ chosen stochastically according to the equilibrium distribution of Markov chain representing the random walk is called Kemeny constant, which is…
A sorting network is a shortest path from $12\dots n$ to $n\dots 21$ in the Cayley graph of the symmetric group $\mathfrak S_n$ spanned by adjacent transpositions. The paper computes the edge local limit of the uniformly random sorting…
Transportation and distribution networks are a class of spatial networks that have been of interest in recent years. These networks are often characterized by the presence of complex structures such as central loops paired with peripheral…
We prove that the simple random walk on the uniform infinite planar triangulation (UIPT) typically travels graph distance at most $n^{1/4 + o_n(1)}$ in $n$ units of time. Together with the complementary lower bound proven by Gwynne and…
We study random graphs with an i.i.d. degree sequence of which the tail of the distribution function $F$ is regularly varying with exponent $\tau\in (1,2)$. Thus, the degrees have infinite mean. Such random graphs can serve as models for…
The focus of this work is the asymptotic analysis of the tail distribution of Google's PageRank algorithm on large scale-free directed networks. In particular, the main theorem provides the convergence, in the Kantorovich-Rubinstein metric,…
Recently similarity graphs became the leading paradigm for efficient nearest neighbor search, outperforming traditional tree-based and LSH-based methods. Similarity graphs perform the search via greedy routing: a query traverses the graph…
This paper is about the construction of displacement interpolations on a discrete metric graph. Our approach is based on the approximation of any optimal transport problem whose cost function is a distance on a discrete graph by a sequence…
Epidemic modeling has been extensively used in the last years in the field of telecommunications and computer networks. We consider the popular Susceptible-Infected-Susceptible spreading model as the metric for information spreading. In…
Path planning is a fundamental problem in road networks, with the goal of finding a path that optimizes objectives such as shortest distance or minimal travel time. Existing methods typically use graph indexing to ensure the efficiency of…
We study the problem of low-stretch spanning trees in graphs of bounded width: bandwidth, cutwidth, and treewidth. We show that any simple connected graph $G$ with a linear arrangement of bandwidth $b$ can be embedded into a distribution…
We performed a large-scale crawl of the World Wide Web, covering 6.9 Million domains and 57 Million subdomains, including all high-traffic sites of the Internet. We present a study of the correlations found between quantities measuring the…
The small-world property is known to have a profound effect on the navigation efficiency of complex networks [J. M. Kleinberg, Nature 406, 845 (2000)]. Accordingly, the proper addition of shortcuts to a regular substrate can lead to the…
For a connected graph $G$, an instance $I$ is a set of pairs of vertices and a corresponding routing $R$ is a set of paths specified for all vertex-pairs in $I$. Let $\mathfrak{R}_I$ be the collection of all routings with respect to $I$.…
The routing number is a graph invariant introduced by Alon, Chung, and Graham in 1994, and it has been studied for trees and other classes of graphs such as hypercubes. It gives the minimum number of routing steps needed to sort a set of…
Distributed network optimization algorithms, such as minimum spanning tree, minimum cut, and shortest path, are an active research area in distributed computing. This paper presents a fast distributed algorithm for such problems in the…
We study spatial networks constructed by randomly placing nodes on a manifold and joining two nodes with an edge whenever their distance is less than a certain cutoff. We derive the general expression for the connectivity distribution of…
We present analytical results for the distribution of shortest path lengths between random pairs of nodes in configuration model networks. The results, which are based on recursion equations, are shown to be in good agreement with numerical…
The recent publication of the `InterTubes' map of long-haul fiber-optic cables in the contiguous United States invites an exciting question: how much faster would the Internet be if routes were chosen to minimize latency? Previous…
In this paper we present an analytic study of sampled networks in the case of some important shortest-path sampling models. We present analytic formulas for the probability of edge discovery in the case of an evolving and a static network…