3,186 research outputs found
Greedy routing and virtual coordinates for future networks
At the core of the Internet, routers are continuously struggling with
ever-growing routing and forwarding tables. Although hardware advances
do accommodate such a growth, we anticipate new requirements e.g. in
data-oriented networking where each content piece has to be referenced
instead of hosts, such that current approaches relying on global
information will not be viable anymore, no matter the hardware
progress. In this thesis, we investigate greedy routing methods that
can achieve similar routing performance as today but use much less
resources and which rely on local information only. To this end, we
add specially crafted name spaces to the network in which virtual
coordinates represent the addressable entities. Our scheme enables participating
routers to make forwarding decisions using only neighbourhood information,
as the overarching pseudo-geometric name space structure already
organizes and incorporates "vicinity" at a global level.
A first challenge to the application of greedy routing on virtual
coordinates to future networks is that of "routing dead-ends"
that are local minima due to the difficulty of consistent coordinates
attribution. In this context, we propose a routing recovery scheme
based on a multi-resolution embedding of the network in low-dimensional Euclidean spaces.
The recovery is performed by routing greedily on a blurrier view of the network. The
different network detail-levels are obtained though the embedding of
clustering-levels of the graph. When compared with
higher-dimensional embeddings of a given network, our method shows a
significant diminution of routing failures for similar header and
control-state sizes.
A second challenge to the application of virtual coordinates and
greedy routing to future networks is the support of
"customer-provider" as well as "peering" relationships between
participants, resulting in a differentiated services
environment. Although an application of greedy routing within such a
setting would combine two very common fields of today's networking
literature, such a scenario has, surprisingly, not been studied so
far. In this context we propose two approaches to address this scenario.
In a first approach we implement a path-vector protocol similar to
that of BGP on top of a greedy embedding of the network. This allows
each node to build a spatial map associated with each of its
neighbours indicating the accessible regions. Routing is then
performed through the use of a decision-tree classifier taking the
destination coordinates as input. When applied on a real-world dataset
(the CAIDA 2004 AS graph) we demonstrate an up to 40% compression ratio of
the routing control information at the network's core as well as a computationally efficient
decision process comparable to methods such as binary trees and tries.
In a second approach, we take inspiration from consensus-finding in social
sciences and transform the three-dimensional distance data structure
(where the third dimension encodes the service differentiation) into a
two-dimensional matrix on which classical embedding tools can be used.
This transformation is achieved by agreeing on a set of
constraints on the inter-node distances guaranteeing an
administratively-correct greedy routing. The computed distances are
also enhanced to encode multipath support. We demonstrate a good
greedy routing performance as well as an above 90% satisfaction of multipath constraints
when relying on the non-embedded obtained distances on synthetic datasets.
As various embeddings of the consensus distances do not fully exploit their multipath potential, the use of compression techniques such as transform coding to
approximate the obtained distance allows for better routing performances
Single failure resiliency in greedy routing
Using greedy routing, network nodes forward packets towards neighbors which are closer to their destination. This approach makes greedy routers significantly more memory-efficient than traditional IP-routers using longest-prefix matching. Greedy embeddings map network nodes to coordinates, such that greedy routing always leads to the destination. Prior works showed that using a spanning tree of the network topology, greedy embeddings can be found in different metric spaces for any graph. However, a single link/node failure might affect the greedy embedding and causes the packets to reach a dead end. In order to cope with network failures, existing greedy methods require large resources and cause significant loss in the quality of the routing (stretch loss). We propose efficient recovery techniques which require very limited resources with minor effect on the stretch. As the proposed techniques are protection, the switch-over takes place very fast. Low overhead, simplicity and scalability of the methods make them suitable for large-scale networks. The proposed schemes are validated on large topologies with properties similar to the Internet. The performances of the schemes are compared with an existing alternative referred as gravity pressure routing
Robust geometric forest routing with tunable load balancing
Although geometric routing is proposed as a memory-efficient alternative to traditional lookup-based routing and forwarding algorithms, it still lacks: i) adequate mechanisms to trade stretch against load balancing, and ii) robustness to cope with network topology change.
The main contribution of this paper involves the proposal of a family of routing schemes, called Forest Routing. These are based on the principles of geometric routing, adding flexibility in its load balancing characteristics. This is achieved by using an aggregation of greedy embeddings along with a configurable distance function. Incorporating link load information in the forwarding layer enables load balancing behavior while still attaining low path stretch. In addition, the proposed schemes are validated regarding their resilience towards network failures
Scalable Routing Easy as PIE: a Practical Isometric Embedding Protocol (Technical Report)
We present PIE, a scalable routing scheme that achieves 100% packet delivery
and low path stretch. It is easy to implement in a distributed fashion and
works well when costs are associated to links. Scalability is achieved by using
virtual coordinates in a space of concise dimensionality, which enables greedy
routing based only on local knowledge. PIE is a general routing scheme, meaning
that it works on any graph. We focus however on the Internet, where routing
scalability is an urgent concern. We show analytically and by using simulation
that the scheme scales extremely well on Internet-like graphs. In addition, its
geometric nature allows it to react efficiently to topological changes or
failures by finding new paths in the network at no cost, yielding better
delivery ratios than standard algorithms. The proposed routing scheme needs an
amount of memory polylogarithmic in the size of the network and requires only
local communication between the nodes. Although each node constructs its
coordinates and routes packets locally, the path stretch remains extremely low,
even lower than for centralized or less scalable state-of-the-art algorithms:
PIE always finds short paths and often enough finds the shortest paths.Comment: This work has been previously published in IEEE ICNP'11. The present
document contains an additional optional mechanism, presented in Section
III-D, to further improve performance by using route asymmetry. It also
contains new simulation result
NextBestOnce: Achieving Polylog Routing despite Non-greedy Embeddings
Social Overlays suffer from high message delivery delays due to insufficient
routing strategies. Limiting connections to device pairs that are owned by
individuals with a mutual trust relationship in real life, they form topologies
restricted to a subgraph of the social network of their users. While
centralized, highly successful social networking services entail a complete
privacy loss of their users, Social Overlays at higher performance represent an
ideal private and censorship-resistant communication substrate for the same
purpose.
Routing in such restricted topologies is facilitated by embedding the social
graph into a metric space. Decentralized routing algorithms have up to date
mainly been analyzed under the assumption of a perfect lattice structure.
However, currently deployed embedding algorithms for privacy-preserving Social
Overlays cannot achieve a sufficiently accurate embedding and hence
conventional routing algorithms fail. Developing Social Overlays with
acceptable performance hence requires better models and enhanced algorithms,
which guarantee convergence in the presence of local optima with regard to the
distance to the target.
We suggest a model for Social Overlays that includes inaccurate embeddings
and arbitrary degree distributions. We further propose NextBestOnce, a routing
algorithm that can achieve polylog routing length despite local optima. We
provide analytical bounds on the performance of NextBestOnce assuming a
scale-free degree distribution, and furthermore show that its performance can
be improved by more than a constant factor when including Neighbor-of-Neighbor
information in the routing decisions.Comment: 23 pages, 2 figure
Self-organized Emergence of Navigability on Small-World Networks
This paper mainly investigates why small-world networks are navigable and how
to navigate small-world networks. We find that the navigability can naturally
emerge from self-organization in the absence of prior knowledge about
underlying reference frames of networks. Through a process of information
exchange and accumulation on networks, a hidden metric space for navigation on
networks is constructed. Navigation based on distances between vertices in the
hidden metric space can efficiently deliver messages on small-world networks,
in which long range connections play an important role. Numerical simulations
further suggest that high cluster coefficient and low diameter are both
necessary for navigability. These interesting results provide profound insights
into scalable routing on the Internet due to its distributed and localized
requirements.Comment: 3 figure
Navigability of temporal networks in hyperbolic space
Information routing is one of the main tasks in many complex networks with a
communication function. Maps produced by embedding the networks in hyperbolic
space can assist this task enabling the implementation of efficient navigation
strategies. However, only static maps have been considered so far, while
navigation in more realistic situations, where the network structure may vary
in time, remain largely unexplored. Here, we analyze the navigability of real
networks by using greedy routing in hyperbolic space, where the nodes are
subject to a stochastic activation-inactivation dynamics. We find that such
dynamics enhances navigability with respect to the static case. Interestingly,
there exists an optimal intermediate activation value, which ensures the best
trade-off between the increase in the number of successful paths and a limited
growth of their length. Contrary to expectations, the enhanced navigability is
robust even when the most connected nodes inactivate with very high
probability. Finally, our results indicate that some real networks are
ultranavigable and remain highly navigable even if the network structure is
extremely unsteady. These findings have important implications for the design
and evaluation of efficient routing protocols that account for the temporal
nature of real complex networks.Comment: 10 pages, 4 figures. Includes Supplemental Informatio
Greedy Forwarding in Dynamic Scale-Free Networks Embedded in Hyperbolic Metric Spaces
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
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