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

A scalable, resilient, and self-managing layer-2 network

textLarge-scale layer-2 Ethernet networks are needed for important future and current applications and services including: metro Ethernet, wide area Ethernet, data center networks, cyber-physical systems, and large data processing. However Ethernet bridging was designed for small local area networks and suffers scalability and resiliency problems for large networks. I will present the architecture and protocols of ROME, a layer-2 network designed to be backwards compatible with Ethernet and scalable to tens of thousands of switches and millions of end hosts. We first design a scalable greedy routing protocol, Multi-hop Delaunay Triangulation (MDT) routing, for delivery guarantee on any connectivity graph with arbitrary node coordinates. To achieve near-optimal routing path for greedy routing, we then present the first layer-2 virtual positioning protocol, Virtual Position on Delaunay (VPoD). We then design a stateless multicast protocol, to support group communication such as VLAN while improving switch memory scalability. To achieve efficient host discovery, we present a novel distributed hash table, Delaunay DHT (D²HT). ROME also includes routing and host discovery protocols for a hierarchical network. ROME protocols completely eliminate broadcast. Extensive experimental results show that ROME protocols are efficient and scalable to metropolitan size. Furthermore, ROME protocols are highly resilient to network dynamics. The routing latency of ROME is only slightly higher than shortest-path latency.Computer Science

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

Graph embeddings for low-stretch greedy routing

The simplest greedy geometric routing forwards packets to make most progress in terms of geometric distance within reach. Its notable advantages are low complexity, and the use of local information only. However, two problems of greedy routing are that delivery is not always guaranteed, and that the greedy routes may take more hops than the corresponding shortest paths. Additionally, in dynamic multihop networks, routing elements can join or leave during network operation or exhibit intermittent failures. Even a single link or node removal may invalidate the greedy routing success guarantees. Greedy embedding is a graph embedding that makes the simple greedy packet forwarding successful for every source-destination pair. In this dissertation, we consider the problems of designing greedy graph embeddings that also yield low hop stretch of the greedy paths over the shortest paths and can accommodate network dynamics. In the first part of the dissertation, we consider embedding and routing for arbitrary unweighted network graphs, based on greedy routing and utilizing virtual node coordinates. We propose an algorithm for online greedy graph embedding in the hyperbolic plane that enables incremental embedding of network nodes as they join the network, without disturbing the global embedding. As an alternative to frequent reembedding of temporally dynamic network graphs in order to retain the greedy embedding property, we propose a simple but robust generalization of greedy geometric routing called Gravity--Pressure (GP) routing. Our routing method always succeeds in finding a route to the destination provided that a path exists, even if a significant fraction of links or nodes is removed subsequent to the embedding. GP routing does not require precomputation or maintenance of special spanning subgraphs and is particularly suitable for operation in tandem with our proposed algorithm for online graph embedding. In the second part of the dissertation we study how topological and geometric properties of embedded graphs influence the hop stretch. Based on the obtained insights, we synthesize embedding heuristics that yield minimal hop stretch greedy embeddings. Finally, we verify their effectiveness on models of synthetic graphs as well as instances of several classes of real-world network graphs

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

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

Overlay Addressing and Routing System Based on Hyperbolic Geometry

International audienceLocal knowledge routing schemes based on virtual coordinates taken from the hyperbolic plane have attracted considerable interest in recent years. In this paper, we propose a new approach for seizing the power of the hyperbolic geometry. We aim at building a scalable and reliable system for creating and managing overlay networks over the Internet. The system is implemented as a peer-to-peer infrastructure based on the transport layer connections between the peers. Through analysis, we show the limitations of the Poincaré disk model for providing virtual coordinates. Through simulations, we assess the practicability of our proposal. Results show that peer-to-peer overlays based on hyperbolic geometry have acceptable performances while introducing scalability and flexibility in dynamic peer-to-peer overlay networks

Space Shuffle: A Scalable, Flexible, and High-Bandwidth Data Center Network

Data center applications require the network to be scalable and bandwidth-rich. Current data center network architectures often use rigid topologies to increase network bandwidth. A major limitation is that they can hardly support incremental network growth. Recent work proposes to use random interconnects to provide growth flexibility. However routing on a random topology suffers from control and data plane scalability problems, because routing decisions require global information and forwarding state cannot be aggregated. In this paper we design a novel flexible data center network architecture, Space Shuffle (S2), which applies greedy routing on multiple ring spaces to achieve high-throughput, scalability, and flexibility. The proposed greedy routing protocol of S2 effectively exploits the path diversity of densely connected topologies and enables key-based routing. Extensive experimental studies show that S2 provides high bisectional bandwidth and throughput, near-optimal routing path lengths, extremely small forwarding state, fairness among concurrent data flows, and resiliency to network failures

Fuzzy and Position Particle Swarm Optimized Routing in VANET

In Intelligent Transport Systems, traffic management and providing stable routing paths between vehicles using vehicular ad hoc networks (VANET\u27s) is critical. Lots of research and several routing techniques providing a long path lifetime have been presented to resolve this issue. However, the routing algorithms suffer excessive overhead or collisions when solving complex optimization problems. In order to improve the routing efficiency and performance in the existing schemes, a Position Particle Swarm Optimization based on Fuzzy Logic (PPSO-FL) method is presented for VANET that provides a high-quality path for communication between nodes. The PPSO-FL has two main steps. The first step is selecting candidate nodes through collectively coordinated metrics using the fuzzy logic technique, improving packet delivery fraction, and minimizing end-to-end delay. The second step is the construction of an optimized routing model. The optimized routing model establishes an optimal route through the candidate nodes using position-based particle swarm optimization. The proposed work is simulated using an NS2 simulator. Simulation results demonstrate that the method outperforms the standard routing algorithms in packet delivery fraction, end-to-end delay and execution time for routing in VANET scenarios