In this paper we study a model for ad-hoc networks close enough to reality as to represent existing networks, being at the same time concise enough to promote strong theoretical results. The Quasi Unit Disk Graph model contains all edges shorter than a parameter d between 0 and 1 and no edges longer than 1. We show that -- in comparison to the cost known on Unit Disk Graphs -- the complexity results in this model contain the additional factor 1/d². We prove that in Quasi Unit Disk Graphs flooding is an asymptotically message-optimal routing technique, provide a geometric routing algorithm being more efficient above all in dense networks, and show that classic geometric routing is possible with the same performance guarantees as for Unit Disk Graphs if d 1/ # 2.

It was recently reported that all known face and combined greedy-face routing variants cannot guarantee message delivery in arbitrary undirected planar graphs. The purpose of this article is to clarify that this is not the truth in general. We show that specifically in relative neighborhood and Gabriel graphs recovery from a greedy routing failure is always possible without changing between any adjacent faces. Guaranteed delivery then follows from guaranteed recovery while traversing the very first face. In arbitrary graphs, however, a proper face selection mechanism is of importance since recovery from a greedy routing failure may require visiting a sequence of faces before greedy routing can be restarted again. A prominent approach is to visit a sequence of faces which are intersected by the line connecting the source and destination node. Whenever encountering an edge which is intersecting with this line, the critical part is to decide if face traversal has to change to the next adjacent one or not. Failures may occur from incorporating face routing procedures that force to change the traversed face at each intersection. Recently observed routing failures which were produced by the GPSR protocol in arbitrary planar graphs result from incorporating such a face routing variant. They cannot be constructed by the well known GFG algorithm which does not force changing the face anytime. Beside methods which visit the faces intersected by the source destination line, we discuss face routing variants which simply restart face routing whenever the next face has to be explored. We give the first complete and formal proofs that several proposed face routing, and combined greedyface routing schemes do guarantee delivery in specific graph classes or even any arbitrary planar graphs. We also discuss the reasons why other methods may fail to deliver a message or even end up in a loop.

We present a new geographic routing algorithm, Greedy Distributed Spanning Tree Routing (GDSTR), that finds shorter routes and generates less maintenance traffic than previous algorithms. While geographic routing potentially scales well, it faces the problem of what to do at local dead ends where greedy forwarding fails. Existing geographic routing algorithms handle dead ends by planarizing the node connectivity graph and then using the right-hand rule to route around the resulting faces. GDSTR handles this

Routing protocols for wireless sensor networks must address the challenges of reliable packet delivery at increasingly large scale and highly constrained node resources. Attempts to limit node state can result in undesirable worst-case routing performance, as measured by stretch, which is the ratio of the hop count of the selected path to that of the optimal path. We present a new routing protocol, Small State and Small Stretch (S4),which jointly minimizes the state and stretch. S4 uses a combination of beacon distance-vector based global routing state and scoped distance-vector based local routing state to achieve a worst-case stretch of 3 using O ( √ N) routing state per node in an N-node network. Its average routing stretch is close to 1. S4 further incorporates local failure recovery to achieve resilience to dynamic topology changes. We use multiple simulation environments to assess performance claims at scale, and use experiments in a 42-node wireless sensor network testbed to evaluate performance under realistic RF and failure dynamics. The results show that S4 achieves scalability, efficiency, and resilience in a wide range of scenarios. 1

Abstract—We study the problem of landmark selection for landmark-based routing in a network of fixed wireless communication nodes. We present a distributed landmark selection algorithm that does not rely on global clock synchronization, and a companion local greedy landmark-based routing scheme. We assume no node location information, and that each node can communicate with some of its geographic neighbors. Each node is named by its hop count distances to a small number of nearby landmarks. Greedy routing at a node is performed to equalize its vector of landmark distances to that of the destination. This is done by following the shortest path to the landmark that maximizes the ratio of its distances to the source and the destination. In addition, we propose a method to alleviate the difficulty in routing to destinations near the boundaries by virtually expanding the network boundaries. The greedy routing, when combined with our landmark selection scheme, has a provable bounded path stretch relative to the best path possible, and guarantees packet delivery in the continuous domain. In the discrete domain, our simulations show that the landmark selection scheme is effective, and the companion routing scheme performs well under realistic settings. Both the landmark selection and greedy routing assumes no specific communication model and works with asymmetric links. Although some of the analysis are non-trivial, the algorithms are simple, flexible and cost-effective enough to warrant a real-world deployment. I.

Abstract—We consider the problem of throughput-optimal routing over large-scale wireless ad-hoc networks. Gupta and Kumar (2000) showed that a throughput capacity (a uniform 1) is achievable n log n rate over all source-destination pairs) of Θ( in random planar networks, and the capacity is achieved by straight-line routes. In reality, both the network model and the traffic demands are likely to be highly non-uniform. In this paper, we first propose a randomized forwarding strategy based on geographic routing that achieves near-optimal throughput over random planar networks with an arbitrary number of routing holes (regions devoid of nodes) of varying sizes. Next, we study a random planar network with arbitrary source-destination pairs with arbitrary traffic demands. For such networks, we demonstrate a randomized local load-balancing algorithm that supports any traffic load that is within a poly-logarithmic factor of the throughput region. Our algorithms are based on geographic routing and hence inherit their advantageous properties of lowcomplexity, robustness and stability. I.

Abstract—The one type of routing in ad hoc and sensor networks that currently appears to be most amenable to algorithmic analysis is geographic routing. This paper contains an introduction to the problem field of geographic routing, presents a specific routing algorithm based on a synthesis of the greedy forwarding and face routing approaches, and provides an algorithmic analysis of the presented algorithm from both a worst-case and an average-case perspective. Index Terms—Algorithmic analysis, routing, stretch, wireless networks.

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Many recently proposed sensornet applications require large number of sensor nodes operating over long periods of time. In contrast to the first-generation sensornet deployments, these applications involve sophisticated internode communication rather than simple tree-based data collection. The examples include network maintenance, data-centric storage, object tracking, and various query engines. If these proposals for next-generation applications are ever to become reality, we will need solutions for self-organization of very large networks. We argue that these applications need methods for organizing nodes into recursive geometric structures, for example, proximity-based hierarchies. Such structures should provide naming that facilitates amongst others, routing, multicasting, and data aggregation and fusion. This paper presents a novel algorithm for dynamically organizing nodes in a sensornet into an area hierarchy. The algorithm employs gossiping, guaranteeing predictable maintenance traffic, which is a crucial property when it comes to energy conservation. Simulations show that the algorithm scales to large networks, works well in the presence of message loss and network

Abstract. We present a concurrent face routing CFR algorithm. We formally prove that the worst case latency of our algorithm is asymptotically optimal. Our simulation results demonstrate that, on average, CFR significantly outperforms the best known geometric routing algorithms in the path stretch: the speed of message delivery. Its performance approaches the shortest possible path. CFR maintains its advantage over the other algorithms in pure form as well as in combination with greedy routing; on planar as well as on non-planar graphs. Key words: geometric routing, ad hoc wireless routing 1