MAP: Medial Axis Based Geometric Routing in Sensor Networks

One of the challenging tasks in the deployment of dense wireless networks (like sensor networks) is in devising a routing scheme for node to node communication. Important consideration includes scalability, routing complexity, the length of the communication paths and the load sharing of the routes. In this paper, we show that a compact and expressive abstraction of network connectivity by the medial axis enables efficient and localized routing. We propose MAP, a Medial Axis based naming and routing Protocol that does not require locations, makes routing decisions locally, and achieves good load balancing. In its preprocessing phase, MAP constructs the medial axis of the sensor field, defined as the set of nodes with at least two closest boundary nodes. The medial axis of the network captures both the complex geometry and non-trivial topology of the sensor field. It can be represented compactly by a graph whose size is comparable with the complexity of the geometric features (e.g., the number of holes). Each node is then given a name related to its position with respect to the medial axis. The routing scheme is derived through local decisions based on the names of the source and destination nodes and guarantees delivery with reasonable and natural routes. We show by both theoretical analysis and simulations that our medial axis based geometric routing scheme is scalable, produces short routes, achieves excellent load balancing, and is very robust to variations in the network model

DMFSGD: A Decentralized Matrix Factorization Algorithm for Network Distance Prediction

The knowledge of end-to-end network distances is essential to many Internet applications. As active probing of all pairwise distances is infeasible in large-scale networks, a natural idea is to measure a few pairs and to predict the other ones without actually measuring them. This paper formulates the distance prediction problem as matrix completion where unknown entries of an incomplete matrix of pairwise distances are to be predicted. The problem is solvable because strong correlations among network distances exist and cause the constructed distance matrix to be low rank. The new formulation circumvents the well-known drawbacks of existing approaches based on Euclidean embedding. A new algorithm, so-called Decentralized Matrix Factorization by Stochastic Gradient Descent (DMFSGD), is proposed to solve the network distance prediction problem. By letting network nodes exchange messages with each other, the algorithm is fully decentralized and only requires each node to collect and to process local measurements, with neither explicit matrix constructions nor special nodes such as landmarks and central servers. In addition, we compared comprehensively matrix factorization and Euclidean embedding to demonstrate the suitability of the former on network distance prediction. We further studied the incorporation of a robust loss function and of non-negativity constraints. Extensive experiments on various publicly-available datasets of network delays show not only the scalability and the accuracy of our approach but also its usability in real Internet applications.Comment: submitted to IEEE/ACM Transactions on Networking on Nov. 201

Greedy routing with guaranteed delivery using Ricci flows

Greedy forwarding with geographical locations in a wireless sensor network may fail at a local minimum. In this paper we propose to use conformal mapping to compute a new embedding of the sensor nodes in the plane such that greedy forwarding with the virtual coordinates guarantees delivery. In particular, we extract a planar triangulation of the sensor network with non-triangular faces as holes, by either using the nodes ’ location or using a landmark-based scheme without node location. The conformal map is computed with Ricci flow such that all the non-triangular faces are mapped to perfect circles. Thus greedy forwarding will never get stuck at an intermediate node. The computation of the conformal map and the virtual coordinates is performed at a preprocessing phase and can be implemented by local gossip-style computation. The method applies to both unit disk graph models and quasi-unit disk graph models. Simulation results are presented for these scenarios

Modeling Distances in Large-Scale Networks by Matrix Factorization

In this paper, we propose a model for representing and predicting distances in large-scale networks by matrix factorization. The model is useful for network distance sensitive applications, such as content distribution networks, topology-aware overlays, and server selections. Our approach overcomes several limitations of previous coordinates-based mechanisms, which cannot model sub-optimal routing or asymmetric routing policies. We describe two algorithms -- singular value decomposition (SVD) and nonnegative matrix factorization (NMF) -- for representing a matrix of network distances as the product of two smaller matrices. With such a representation, we build a scalable system -- Internet Distance Estimation Service (IDES) -- that predicts large numbers of network distances from limited numbers of measurements. Extensive simulations on real-world data sets show that IDES leads to more accurate, efficient and robust predictions of latencies in large-scale networks than previous approaches

Reducing Congestion Effects by Multipath Routing in Wireless Networks

We propose a solution to improve fairness and increasethroughput in wireless networks with location information.Our approach consists of a multipath routing protocol, BiasedGeographical Routing (BGR), and two congestion controlalgorithms, In-Network Packet Scatter (IPS) and End-to-EndPacket Scatter (EPS), which leverage BGR to avoid the congestedareas of the network. BGR achieves good performancewhile incurring a communication overhead of just 1 byte perdata packet, and has a computational complexity similar togreedy geographic routing. IPS alleviates transient congestion bysplitting traffic immediately before the congested areas. In contrast,EPS alleviates long term congestion by splitting the flow atthe source, and performing rate control. EPS selects the pathsdynamically, and uses a less aggressive congestion controlmechanism on non-greedy paths to improve energy efficiency.Simulation and experimental results show that our solutionachieves its objectives. Extensive ns-2 simulations show that oursolution improves both fairness and throughput as compared tosingle path greedy routing. Our solution reduces the variance ofthroughput across all flows by 35%, reduction which is mainlyachieved by increasing throughput of long-range flows witharound 70%. Furthermore, overall network throughput increasesby approximately 10%. Experimental results on a 50-node testbed are consistent with our simulation results, suggestingthat BGR is effective in practice

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

Using Internet Geometry to Improve End-to-End Communication Performance

The Internet has been designed as a best-effort communication medium between its users, providing connectivity but optimizing little else. It does not guarantee good paths between two users: packets may take longer or more congested routes than necessary, they may be delayed by slow reaction to failures, there may even be no path between users. To obtain better paths, users can form routing overlay networks, which improve the performance of packet delivery by forwarding packets along links in self-constructed graphs. Routing overlays delegate the task of selecting paths to users, who can choose among a diversity of routes which are more reliable, less loaded, shorter or have higher bandwidth than those chosen by the underlying infrastructure. Although they offer improved communication performance, existing routing overlay networks are neither scalable nor fair: the cost of measuring and computing path performance metrics between participants is high (which limits the number of participants) and they lack robustness to misbehavior and selfishness (which could discourage the participation of nodes that are more likely to offer than to receive service). In this dissertation, I focus on finding low-latency paths using routing overlay networks. I support the following thesis: it is possible to make end-to-end communication between Internet users simultaneously faster, scalable, and fair, by relying solely on inherent properties of the Internet latency space. To prove this thesis, I take two complementary approaches. First, I perform an extensive measurement study in which I analyze, using real latency data sets, properties of the Internet latency space: the existence of triangle inequality violations (TIVs) (which expose detour paths: ''indirect'' one-hop paths that have lower round-trip latency than the ''direct'' default paths), the interaction between TIVs and network coordinate systems (which leads to scalable detour discovery), and the presence of mutual advantage (which makes fairness possible). Then, using the results of the measurement study, I design and build PeerWise, the first routing overlay network that reduces end-to-end latency between its participants and is both scalable and fair. I evaluate PeerWise using simulation and through a wide-area deployment on the PlanetLab testbed

PALM: Predicting Internet Network Distances Using Peer-to-Peer Measurements

Landmark-based architecture has been commonly adopted in the networking community as a mechanism to measure and characterize a host's location on the Internet. In most existing landmark based approaches, end hosts use the distance measurements to a common, fixed set of landmarks to derive an estimated location on the Internet. This paper investigates whether it is possible for participating peer nodes in an overlay network to collaboratively construct an accurate geometric model of its topology in a completely decentralized peer-to-peer fashion, without using a fixed set of landmarks. We call such a peer-to-peer approach in topology discovery and modeling using landmarks PALM (Peers As LandMarks). We evaluate the performance characteristics of such a decentralized coordinates-based approach under several factors, including dimensionality of the geometric space, peer distance distribution, and the number of peer-to-peer distance measurements used. We evaluate two PALM-based schemes: RAND-PALM and ISLAND. In RAND-PALM, a peer node randomly selects from existing peer nodes as its landmarks. In ISLAND (Intelligent Selection of Landmarks), each peer node selects its landmarks by exploiting the topological information derived based on existing peer nodes' coordinates values.Singapore-MIT Alliance (SMA