Bottleneck Discovery and Overlay Management in Network Coded Peer-to-Peer Systems

The performance of peer-to-peer (P2P) networks depends critically on the good connectivity of the overlay topology. In this paper we study P2P networks for content distribution (such as Avalanche) that use randomized network coding techniques. The basic idea of such systems is that peers randomly combine and exchange linear combinations of the source packets. A header appended to each packet specifes the linear combination that the packet carries. In this paper we show that the linear combinations a node receives from its neighbors reveal structural information about the network. We propose algorithms to utilize this observation for topology management to avoid bottlenecks and clustering in network-coded P2P systems. Our approach is decentralized, inherently adapts to the network topology, and reduces substantially the number of topology rewirings that are necessary to maintain a well connected overlay. Moreover, this is done passively during the normal content distribution. This work demonstrates another value of using network coding and complements previous work that showed network coding achieves high utilization of the network resources

Systematic Topology Analysis and Generation Using Degree Correlations

We present a new, systematic approach for analyzing network topologies. We first introduce the dK-series of probability distributions specifying all degree correlations within d-sized subgraphs of a given graph G. Increasing values of d capture progressively more properties of G at the cost of more complex representation of the probability distribution. Using this series, we can quantitatively measure the distance between two graphs and construct random graphs that accurately reproduce virtually all metrics proposed in the literature. The nature of the dK-series implies that it will also capture any future metrics that may be proposed. Using our approach, we construct graphs for d=0,1,2,3 and demonstrate that these graphs reproduce, with increasing accuracy, important properties of measured and modeled Internet topologies. We find that the d=2 case is sufficient for most practical purposes, while d=3 essentially reconstructs the Internet AS- and router-level topologies exactly. We hope that a systematic method to analyze and synthesize topologies offers a significant improvement to the set of tools available to network topology and protocol researchers.Comment: Final versio

Graph Annotations in Modeling Complex Network Topologies

The coarsest approximation of the structure of a complex network, such as the Internet, is a simple undirected unweighted graph. This approximation, however, loses too much detail. In reality, objects represented by vertices and edges in such a graph possess some non-trivial internal structure that varies across and differentiates among distinct types of links or nodes. In this work, we abstract such additional information as network annotations. We introduce a network topology modeling framework that treats annotations as an extended correlation profile of a network. Assuming we have this profile measured for a given network, we present an algorithm to rescale it in order to construct networks of varying size that still reproduce the original measured annotation profile. Using this methodology, we accurately capture the network properties essential for realistic simulations of network applications and protocols, or any other simulations involving complex network topologies, including modeling and simulation of network evolution. We apply our approach to the Autonomous System (AS) topology of the Internet annotated with business relationships between ASs. This topology captures the large-scale structure of the Internet. In depth understanding of this structure and tools to model it are cornerstones of research on future Internet architectures and designs. We find that our techniques are able to accurately capture the structure of annotation correlations within this topology, thus reproducing a number of its important properties in synthetically-generated random graphs

Trapping in complex networks

We investigate the trapping problem in Erdos-Renyi (ER) and Scale-Free (SF) networks. We calculate the evolution of the particle density $\rho(t)$ of random walkers in the presence of one or multiple traps with concentration $c$. We show using theory and simulations that in ER networks, while for short times $\rho(t) \propto \exp(-Act)$, for longer times $\rho(t)$ exhibits a more complex behavior, with explicit dependence on both the number of traps and the size of the network. In SF networks we reveal the significant impact of the trap's location: $\rho(t)$ is drastically different when a trap is placed on a random node compared to the case of the trap being on the node with the maximum connectivity. For the latter case we find \rho(t)\propto\exp\left[-At/N^\frac{\gamma-2}{\gamma-1}\av{k}\right] for all $\gamma>2$, where $\gamma$ is the exponent of the degree distribution $P(k)\propto k^{-\gamma}$.Comment: Appendix adde

Search in Complex Networks : a New Method of Naming

We suggest a method for routing when the source does not posses full information about the shortest path to the destination. The method is particularly useful for scale-free networks, and exploits its unique characteristics. By assigning new (short) names to nodes (aka labelling) we are able to reduce significantly the memory requirement at the routers, yet we succeed in routing with high probability through paths very close in distance to the shortest ones.Comment: 5 pages, 4 figure

Bottleneck Discovery and Overlay Management in Network Coded Peer-to-Peer Systems

The performance of peer-to-peer (P2P) networks depends critically on the good connectivity of the overlay topology. In this paper we study P2P networks for content distribution (such as Avalanche) that use randomized network coding techniques. The basic idea of such systems is that peers randomly combine and exchange linear combinations of the source packets. A header appended to each packet specifies the linear combination that the packet carries. In this paper we show that the linear combinations a node receives from its neighbors reveal structural information about the network. We propose algorithms to utilize this observation for topology management to avoid bottlenecks and clustering in network-coded P2P systems. Our approach is decentralized, inherently adapts to the network topology, and reduces substantially the number of topology rewirings that are necessary to maintain a well connected overlay. Moreover, this is done passively during the normal content distribution. This work demonstrates another value of using network coding and complements previous work that showed network coding achieves high utilization of the network resources

Tailored graph ensembles as proxies or null models for real networks I: tools for quantifying structure

We study the tailoring of structured random graph ensembles to real networks, with the objective of generating precise and practical mathematical tools for quantifying and comparing network topologies macroscopically, beyond the level of degree statistics. Our family of ensembles can produce graphs with any prescribed degree distribution and any degree-degree correlation function, its control parameters can be calculated fully analytically, and as a result we can calculate (asymptotically) formulae for entropies and complexities, and for information-theoretic distances between networks, expressed directly and explicitly in terms of their measured degree distribution and degree correlations.Comment: 25 pages, 3 figure

Priority diffusion model in lattices and complex networks

We introduce a model for diffusion of two classes of particles ($A$ and $B$) with priority: where both species are present in the same site the motion of $A$'s takes precedence over that of $B$'s. This describes realistic situations in wireless and communication networks. In regular lattices the diffusion of the two species is normal but the $B$ particles are significantly slower, due to the presence of the $A$ particles. From the fraction of sites where the $B$ particles can move freely, which we compute analytically, we derive the diffusion coefficients of the two species. In heterogeneous networks the fraction of sites where $B$ is free decreases exponentially with the degree of the sites. This, coupled with accumulation of particles in high-degree nodes leads to trapping of the low priority particles in scale-free networks.Comment: 5 pages, 3 figure

Multi-user video streaming using unequal error protection network coding in wireless networks

In this paper, we investigate a multi-user video streaming system applying unequal error protection (UEP) network coding (NC) for simultaneous real-time exchange of scalable video streams among multiple users. We focus on a simple wireless scenario where users exchange encoded data packets over a common central network node (e.g., a base station or an access point) that aims to capture the fundamental system behaviour. Our goal is to present analytical tools that provide both the decoding probability analysis and the expected delay guarantees for different importance layers of scalable video streams. Using the proposed tools, we offer a simple framework for design and analysis of UEP NC based multi-user video streaming systems and provide examples of system design for video conferencing scenario in broadband wireless cellular networks