Related papers: Compact Routing on Internet-Like Graphs
Recently, In [Phys. Rev. Lett. 104, 018701 (2010)] the authors studied a spatial network which is constructed from a regular lattice by adding long-range edges (shortcuts) with probability $P_{ij}\sim r_{ij}^{-\alpha}$, where $r_{ij}$ is…
In this paper we theoretically and empirically study the degree and connectivity of the Internet's scale-free topology at the autonomous system (AS) level. The basic features of the scale-free network have influence on the normalization…
Shortest Path (SP) computation is a fundamental operation in many real-life applications such as navigation on road networks, link analysis on social networks, etc. These networks tend to be massive, and graph partitioning is commonly…
In order to investigate the routing aspects of small-world networks, Kleinberg proposes a network model based on a $d$-dimensional lattice with long-range links chosen at random according to the $d$-harmonic distribution. Kleinberg shows…
Graphlets are induced subgraph patterns and have been frequently applied to characterize the local topology structures of graphs across various domains, e.g., online social networks (OSNs) and biological networks. Discovering and computing…
Motivated by the increasing need to understand the algorithmic foundations of distributed large-scale graph computations, we study a number of fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$…
In the standard CONGEST model for distributed network computing, it is known that "global" tasks such as minimum spanning tree, diameter, and all-pairs shortest paths, consume large bandwidth, for their running-time is…
A network topology with low average shortest path length (ASPL) provides efficient data transmission while the number of nodes and the number of links incident to each node are often limited due to physical constraints. In this paper, we…
Emerging reconfigurable optical communication technologies allow to enhance datacenter topologies with demand-aware links optimized towards traffic patterns. This paper studies the algorithmic problem of jointly optimizing topology and…
A class of cubic networks composed of a regular one-dimensional lattice and a set of long-range links is introduced. Networks parametrized by a positive integer k are constructed by starting from a one-dimensional lattice and iteratively…
In a network, the shortest paths between nodes are of great importance as they allow the fastest and strongest interaction between nodes. However measuring the shortest paths between all nodes in a large network is computationally…
We prove that any graph $G$ with $n$ points has a distribution $\mathcal{T}$ over spanning trees such that for any edge $(u,v)$ the expected stretch $E_{T \sim \mathcal{T}}[d_T(u,v)/d_G(u,v)]$ is bounded by $\tilde{O}(\log n)$. Our result…
We present two complementary analytical approaches for calculating the distribution of shortest path lengths in Erdos-R\'enyi networks, based on recursion equations for the shells around a reference node and for the paths originating from…
Random scale-free networks are ultrasmall worlds. The average length of the shortest paths in networks of size N scales as lnlnN. Here we show that these ultrasmall worlds can be navigated in ultrashort time. Greedy routing on scale-free…
The paper presents fault-tolerant (FT) labeling schemes for general graphs, as well as, improved FT routing schemes. For a given $n$-vertex graph $G$ and a bound $f$ on the number of faults, an $f$-FT connectivity labeling scheme is a…
We find that scale-free random networks are excellently modeled by a deterministic graph. This graph has a discrete degree distribution (degree is the number of connections of a vertex) which is characterized by a power-law with exponent…
A Delaunay graph built on a planar point set has an edge between two vertices when there exists a disk with the two vertices on its boundary and no vertices in its interior. When the disk is replaced with an equilateral triangle, the…
We consider the problem of computing compact routing tables for a (weighted) planar graph $G:= (V, E,w)$ in the PRAM, CONGEST, and the novel HYBRID communication model. We present algorithms with polylogarithmic work and communication that…
We review results on the scaling of the optimal path length in random networks with weighted links or nodes. In strong disorder we find that the length of the optimal path increases dramatically compared to the known small world result for…
This paper is concerned with the characterization of the relationship between topology and traffic dynamics. We use a model of network generation that allows the transition from random to scale free networks. Specifically, we consider three…