Routing in NDN networks must scale in terms of forwarding table size and routing protocol overhead. Hyperbolic routing (HR) presents a potential solution to address the routing scalability problem, because it does not use traditional forwarding tables or exchange routing updates upon changes in network topologies. Although HR has the drawbacks of producing sub-optimal routes or local minima for some destinations, these issues can be mitigated by NDN's intelligent data forwarding plane. However, HR's viability still depends on both the quality of the routes HR provides and the overhead incurred at the forwarding plane due to HR's sub-optimal behavior. We designed a new forwarding strategy called Adaptive Smoothed RTT-based Forwarding (ASF) to mitigate HR's sub-optimal path selection. This paper describes our experimental investigation into the packet delivery delay and overhead under HR as compared with Named-Data Link State Routing (NLSR), which calculates shortest paths. We run emulation experiments using various topologies with different failure scenarios, probing intervals, and maximum number of next hops for a name prefix. Our results show that HR's delay stretch has a median close to 1 and a 95th-percentile around or below 2, which does not grow with the network size. HR's message overhead in dynamic topologies is nearly independent of the network size, while NLSR's overhead grows polynomially at least. These results suggest that HR offers a more scalable routing solution with little impact on the optimality of routing paths.

Recent years have shown a promising progress in understanding geometric underpinnings behind the structure, function, and dynamics of many complex networks in nature and society. However, these promises cannot be readily fulfilled and lead to important practical applications, without a simple, reliable, and fast network mapping method to infer the latent geometric coordinates of nodes in a real network. Here, we present HyperMap, a simple method to map a given real network to its hyperbolic space. The method utilizes a recent geometric theory of complex networks modeled as random geometric graphs in hyperbolic spaces. The method replays the network's geometric growth, estimating at each time-step the hyperbolic coordinates of new nodes in a growing network by maximizing the likelihood of the network snapshot in the model. We apply HyperMap to the Autonomous Systems (AS) Internet and find that: 1) the method produces meaningful results, identifying soft communities of ASs belonging to the same geographic region; 2) the method has a remarkable predictive power: Using the resulting map, we can predict missing links in the Internet with high precision, outperforming popular existing methods; and 3) the resulting map is highly navigable, meaning that a vast majority of greedy geometric routing paths are successful and low-stretch. Even though the method is not without limitations, and is open for improvement, it occupies a unique attractive position in the space of tradeoffs between simplicity, accuracy, and computational complexity.

As the Internet autonomous system (AS)-level topology grows over time, some of its structural properties remain unchanged. Such time-invariant properties are generally interesting because they tend to reflect some fundamental processes or constraints behind Internet growth. As has been shown before, the time-invariant structural properties of the Internet include some most basic ones, such as the degree distribution or clustering. Here, we add to this time-invariant list a nontrivial property - k-dense decomposition. This property is derived from a recursive form of edge multiplicity, defined as the number of triangles that share a given edge. We show that after proper normalization, the k-dense decomposition of the Internet has remained stable over the last decade, even though the Internet size has approximately doubled, and so has the k-density of its k-densest core. This core consists mostly of content providers peering at Internet eXchange Points, and it only loosely overlaps with the high-degree or high-rank AS core, consisting mostly of tier-1 transit providers. We thus show that high degrees and high k-densities reflect two different Internet-specific properties of ASs (transit versus content providers). As a consequence, even though degrees and k-densities of nodes are correlated, the relative fluctuations are strong, and related to that, random graphs with the same degree distribution or even degree correlations as in the Internet, do not reproduce its k-dense decomposition. Therefore an interesting open question is what Internet topology models or generators can fully explain or at least reproduce the k-dense properties of the Internet.

We show that complex (scale-free) network topologies naturally emerge from hyperbolic metric spaces. Hyperbolic geometry facilitates maximally efficient greedy forwarding in these networks. Greedy forwarding is topology-oblivious. Nevertheless, greedy packets find their destinations with 100% probability following almost optimal shortest paths. This remarkable efficiency sustains even in highly dynamic networks. Our findings suggest that forwarding information through complex networks, such as the Internet, is possible without the overhead of existing routing protocols, and may also find practical applications in overlay networks for tasks such as application-level routing, information sharing, and data distribution.

Researchers involved in designing network services and protocols rely on results from simulation and emulation environments to understand their application performance and scalability. To better understand the behavior of these applications and predict their performance when deployed on the actual Internet, the generated topologies must closely match real network characteristics, not just in terms of graph structure (node interconnectivity) but also with respect to various node and link annotations. Relevant annotations include link latencies, AS membership and whether a router is a peering or internal router. Finally, it should be possible to rescale a given topology to a variety of sizes while still maintaining its essential characteristics.

Researchers have proposed a variety of metrics to measure important graph properties, for instance, in social, biological, and computer networks. Values for a particular graph metric may capture a graph's resilience to failure or its routing efficiency. Knowledge of appropriate metric values may influence the engineering of future topologies, repair strategies in the face of failure, and understanding of fundamental properties of existing networks. Unfortunately, there are typically no algorithms to generate graphs matching one or more proposed metrics and there is little understanding of the relationships among individual metrics or their applicability to different settings. 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.

The Thorup-Zwick (TZ) compact routing scheme is the first generic stretch-3 routing scheme delivering a nearly optimal per-node memory upper bound. Using both direct analysis and simulation, we derive the stretch distribution of this routing scheme on Internet-like inter-domain topologies. By investigating the TZ scheme on random graphs with power-law node degree distributions, P/sub k//spl sime/k/sup -/spl gamma//, we find that the average TZ stretch is quite low and virtually independent of /spl gamma/. In particular, for the Internet inter-domain graph with /spl gamma//spl sime/2.1, the average TZ stretch is around 1.1, with up to 70% of all pairwise paths being stretch-1 (shortest possible). As the network grows, the average stretch slowly decreases. We find routing table sizes to be very small (around 50 records for 104-node networks), well below their theoretical upper bounds. Furthermore, we find that both the average shortest path length (i.e. distance) d~ and width of the distance distribution /spl sigma/ observed in the real Internet inter-AS graph have values that are very close to the minimums of the average stretch in the d~- and /spl sigma/ -directions. This leads us to the discovery of a unique critical point of the average TZ stretch as a function of d~ and /spl sigma/. The Internet's distance distribution is located in a close neighborhood of this point. This is remarkable given the fact that the Internet inter-domain topology has evolved without any direct attention paid to properties of the stretch distribution. It suggests the average stretch function may be an indirect indicator of the optimization criteria influencing the Internet's inter-domain topology evolution.