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.

Clustering is the unsupervised classification of patterns (observations, data items, or feature vectors) into groups (clusters). The clustering problem has been addressed in many contexts and by researchers in many disciplines; this reflects its broad appeal and usefulness as one of the steps in exploratory data analysis. However, clustering is a difficult problem combinatorially, and differences in assumptions and contexts in different communities has made the transfer of useful generic concepts and methodologies slow to occur. This paper presents an overview of pattern clustering methods from a statistical pattern recognition perspective, with a goal of providing useful advice and references to fundamental concepts accessible to the broad community of clustering practitioners. We present a taxonomy of clustering techniques, and identify cross-cutting themes and recent advances. We also describe some important applications of clustering algorithms such as image segmentation, object recognition, and information retrieval.

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.

Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is sometimes useful or required to compute what one might call the "shape" of the set. For that purpose, this paper introduces the formal notion of the family of ff-shapes of a finite point set in R³. Each shape is a well-defined polytope, derived from the Delaunay triangulation of the point set, with a parameter ff 2 IR controlling the desired level of detail. An algorithm is presented that constructs the entire family of shapes for a given set of size n in time O(n²), worst case. A robust implementation of the algorithm is discussed and several applications in the area of scientific computing are mentioned.

We present an overview of ad-hoc routing protocols that make forwarding decisions based on the geographical position of a packet's destination. Other than the destination 's position, each node needs to know only its own position and the position of its one-hop neighbors in order to forward packets. Since it is not necessary to maintain explicit routes, position-based routing does scale well even if the network is highly dynamic. This is a major advantage in a mobile ad-hoc network where the topology may change frequently. The main prerequisite for position-based routing is that a sender can obtain the current position of the destination. Therefore, recently proposed location services are discussed in addition to position-based packet forwarding strategies. We provide a qualitative comparison of the approaches in both areas and investigate opportunities for future research.

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...

bahl~microsoft, corn ymwang~microsoft, corn rogerwa~microsoft, corn The topology of a wireless multi-hop network can be con-trolled by varying the transmission power at each node. In this paper, we give a detailed analysis of a cone-based dis-tributed topology control algorithm. This algorithm, intro-duced in [16], does not assume that nodes have GPS in-formation available; rather it depends only on directional information. Roughly speaking, the basic idea of the algo-rithm is that a node u transmits with the minimum power P~,,a required to ensure that in every cone of degree a around u, there is some node that u can reach with power Pma- We show that taking a = 57r/6 is a necessary and sufficient con-dition to guarantee that network connectivity is preserved. More precisely, if there is a path from a to t when every node communicates at maximum power then, if a < _ 5~r/6, there is still a path in the smallest symmetric graph Ga con-taining all edges (u, v) such that u can communicate with v using power p~,a. On the other hand, if ~> 51r/6, connec-tivity is not necessarily preserved. We also propose a set of optimizations that further reduce power consumption and prove that they retain network connectivity. Dynamic re-configuration in the presence of failures and mobility is also discussed. Simulation results are presented to demonstrate the effectiveness of the algorithm and the optimizations. 1.

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.