We describe how a set of mobile robots can arrange themselves on any specified curve on the plane in the presence of dynamic changes both in the underlying ad hoc network and in the set of participating robots. Our strategy is for the mobile robots to implement a self-stabilizing virtual layer consisting of mobile client nodes, stationary Virtual Nodes (VNs), and local broadcast communication. The VNs are associated with predetermined regions in the plane and coordinate among themselves to distribute the client nodes relatively uniformly among the VNs' regions. Each VN directs its local client nodes to align themselves on the local portion of the target curve. The resulting motion coordination protocol is self-stabilizing, in that each robot can begin the execution in any arbitrary state and at any arbitrary location in the plane. In addition, self-stabilization ensures that the robots can adapt to changes in the desired target formation.

We introduce a virtual-node based mobile object tracking algorithm for mobile sensor networks, VINESTALK. The algorithm uses the virtual stationary automata programming layer, consisting of mobile clients, virtual timed machines distributed at known locations in the plane, called virtual stationary automata (VSAs), and a communication service connecting VSAs and mobile clients. VINESTALK maintains a data structure on top of an underlying hierarchical partitioning of the network. In a grid partitioning, operations to find a mobile object distance d away take O(d) time and communication to complete. Updates to the tracking structure after the object has moved a total of d distance take O{d*log network diameter) amortized time and communication to complete. The tracked object may relocate without waiting for VINESTALK to complete updates for prior moves, and while a find is in progress.

We consider the fault-tolerant consensus problem in wireless ad hoc networks with crash-prone nodes. We develop consensus algorithms for single-hop environments where the nodes are located within broadcast range of each other. Our algorithms tolerate highly unpredictable wireless communication, in which messages may be lost due to collisions, electromagnetic interference, or other anomalies. Accordingly, each node may receive a different set of messages in the same round. In order to minimize collisions, we design adaptive algorithms that attempt to minimize the broadcast contention. To cope with unreliable communication, we augment the nodes with collision detectors and present a new classification of collision detectors in terms of accuracy and completeness, based on practical realities. We show exactly in which cases consensus can be solved, and thus determine the requirements for a useful collision detector.We validate the feasibility of our algorithms, and the underlying wireless model, with simulations based on a realistic 802.11 MAC layer implementation and a detailed radio propagation model. We analyze the performance of our algorithms under varying sizes and densities of deployment and varying MAC layer parameters. We use our single-hop consensus algorithms as the basis for solving consensus in a multi-hop network, demonstrating the resilience of our algorithms to a challenging and noisy environment.

The task of designing algorithms for constantly changing networks is difficult. We focus on mobile ad-hoc networks, where mobile processors attempt to coordinate despite minimal infrastructure support. We develop new techniques to cope with this dynamic, heterogeneous, and chaotic environment. We mask the unpredictable behavior of mobile networks by defining and emulating a virtual infrastructure, consisting of timing-aware and location-aware machines at fixed locations, that mobile nodes can interact with. The static virtual infrastructure allows appplication developers to use simpler algorithms — including many previously developed for fixed networks. Virtual Stationary Automata programming layer. Our programming abstraction consists of a static infrastructure of fixed, timed virtual machines with an explicit notion of real time, called Virtual Stationary Automata (VSAs), distributed at known locations over the plane, and emulated by the real mobile nodes in the system. Each VSA represents a predetermined geographic area and has broadcast capabilities similar to those of the mobile nodes, allowing nearby VSAs and mobile nodes to communicate with one another. This programming layer provides mobile nodes with a virtual infrastructure with which to coordinate their actions. Many practical algorithms depend significantly on timing, and it is reasonable to assume that many mobile nodes have access to reasonably synchronized clocks. In the VSA programming layer, the virtual automata also have access to virtual clocks, guaranteed to not drift too far from real time. Our virtual infrastructure differs in key ways from others that have previously been proposed for mobile ad-hoc networks. The GeoQuorums algorithm [2] was the first to use virtual nodes; the virtual nodes in that work are atomic objects at fixed geographical locations. More general virtual mobile automata were suggested in [1]; our automata are more powerful than those in [1] in that ours include timing capabilities, which are important for many applications. Also, our automata are stationary, and are arranged in a connected pattern that is similar to a traditional wired ne-

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