karp @ eecs.harvard.edu We present Greedy Perimeter Stateless Routing (GPSR), a novel routing protocol for wireless datagram networks that uses the po-sitions of touters and a packer's destination to make packet for-warding decisions. GPSR makes greedy forwarding decisions us-ing only information about a router's immediate neighbors in the network topology. When a packet reaches a region where greedy forwarding is impossible, the algorithm recovers by routing around the perimeter of the region. By keeping state only about the local topology, GPSR scales better in per-router state than shortest-path and ad-hoc routing protocols as the number of network destinations increases. Under mobility's frequent topology changes, GPSR can use local topology information to find correct new routes quickly. We describe the GPSR protocol, and use extensive simulation of mobile wireless networks to compare its performance with that of Dynamic Source Routing. Our simulations demonstrate GPSR's scalability on densely deployed wireless networks.

We consider routing problems in ad hoc wireless networks modeled as unit graphs in which nodes are points in the plane and two nodes can communicate if the distance between them is less than some fixed unit. We describe the first distributed algorithms for routing that do not require duplication of packets or memory at the nodes and yet guarantee that a packet is delivered to its destination. These algorithms can be extended to yield algorithms for broadcasting and geocasting that do not require packet duplication. A byproduct of our results is a simple distributed protocol for extracting a planar subgraph of a unit graph. We also present simulation results on the performance of our algorithms.

This paper presents a survey of the Voronoi diagram, one of the most fundamental data structures in computational geometry. It demonstrates the importance and usefulness of the Voronoi diagram in a wide variety of fields inside and outside computer science and surveys the history of its development. The paper puts particular emphasis on the unified exposition of its mathematical and algorithmic properties. Finally, the paper provides the first comprehensive bibliography on Voronoi diagrams and related structures.

The Voronoi diagram is a fundamental structure in computationalgeometry and arises naturally in many different fields. This chapter surveys properties of the Voronoi diagram and its geometric dual, the Delaunay triangulation. The emphasis is on practical algorithms for the construction of Voronoi diagrams. 1 Introduction Let S be a set of n points in d-dimensional euclidean space E d . The points of S are called sites. The Voronoi diagram of S splits E d into regions with one region for each site, so that the points in the region for site s2S are closer to s than to any other site in S. The Delaunay triangulation of S is the unique triangulation of S so that there are no elements of S inside the circumsphere of any triangle. Here `triangulation' is extended from the planar usage to arbitrary dimension: a triangulation decomposes the convex hull of S into simplices using elements of S as vertices. The existence and uniqueness of the Delaunay triangulation are perhaps not obvio...

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Geographic routing has been widely hailed as the most promising approach to generally scalable wireless routing. However, the correctness of all currently proposed geographic routing algorithms relies on idealized assumptions about radios and their resulting connectivity graphs. We use testbed measurements to show that these idealized assumptions are grossly violated by real radios, and that these violations cause persistent failures in geographic routing, even on static topologies. Having identified this problem, we then fix it by proposing the Cross-Link Detection Protocol (CLDP), which enables provably correct geographic routing on arbitrary connectivity graphs. We confirm in simulation and further testbed measurements that CLDP is not only correct but practical: it incurs low overhead, exhibits low path stretch, always succeeds in real, static wireless networks, and converges quickly after topology changes. 1

Several localized routing protocols [1] guarantee the delivery of the packets when the underlying network topology is the Delaunay triangulation of all wireless nodes. However, it is expensive to construct the Delaunay triangulation in a distributed manner. Given a set of wireless nodes, we more accurately model the network as a unit-disk graph UDG , in which a link in between two nodes exist only if the distance in between them is at most the maximum transmission range.

In this paper we present AFR, a new geometric mobile adhoc routing algorithm. The algorithm is completely distributed; nodes need to communicate only with direct neighbors in their transmission range. We show that if a best route has cost c, AFR finds a route and terminates with cost O(c ) in the worst case. AFR is the first algorithm with cost bounded by a function of the optimal route. We also give a tight lower bound by showing that any geometric routing algorithm has worst-case ). Thus AFR is asymptotically optimal. We give a non-geometric algorithm that also matches the lower bound, but needs some memory at each node. This establishes an intriguing trade-o# between geometry and memory.

Sensor networks pose a number of challenging conceptual and optimization problems such as location, deployment, and tracking [1]. One of the fundamental problems in sensor networks is the calculation of the coverage. In [1], it is assumed that the sensor has the uniform sensing ability. In this paper, we give efficient distributed algorithms to optimally solve the best-coverage problem raised in [1]. Here, we consider the sensing model: the sensing ability diminishes as the distance increases. As energy conservation is a major concern in wireless (or sensor) networks, we also consider how to find an optimum bestcoverage -path with the least energy consumption. We also consider how to find an optimum best-coverage-path that travels a small distance. In addition, we justify the correctness of the method proposed in [1] that uses the Delaunay triangulation to solve the best coverage problem. Moreover, we show that the search space of the best coverage problem can be confined to the relative neighborhood graph, which can be constructed locally.

und the perimeter of the region. By keeping state only about the local topology, GPSR scales better in per-router state than shortest-path and ad-hoc routing protocols as the number of network destinations increases. Under mobility's frequent topology changes, GPSR can use local topology information to find correct new routes quickly. We describe the GPSR protocol, and use extensive simulation of mobile wireless networks to compare its performance with that of Dynamic Source Routing. Our simulations demonstrate GPSR's iii scalability on densely deployed wireless networks. iv Contents 1 Introduction 1 1.1 Metrics for Evaluating Routing Scalability . . . . . . . . . . . . . . . . . . 3 1.2 Traditional Shortest-Path Algorithms . . . . . . . . . . . . . . . . . . . . . 4 1.3 Ad-Hoc Routing Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Techniques for Routing Scalability . . . . . . . . . . . . . . . . . . . . . . 7 1.5 Applica