A set of identical, mobile agents is deployed in a weighted network. Each agent has a battery--a power source allowing it to move along network edges. An agent uses its battery proportionally to the distance traveled. We consider two tasks: convergecast, in which at the beginning, each agent has some initial piece of information, and information of all agents has to be collected by some agent; and broadcast in which information of one specified agent has to be made available to all other agents. In both tasks, the agents exchange the currently possessed information when they meet. The objective of this paper is to investigate what is the minimal value of power, initially available to all agents, so that convergecast or broadcast can be achieved. We study this question in the centralized and the distributed settings. In the centralized setting, there is a central monitor that schedules the moves of all agents. In the distributed setting every agent has to perform an algorithm being unaware of the network. In the centralized setting, we give a linear-time algorithm to compute the optimal battery power and the strategy using it, both for convergecast and for broadcast, when agents are on the line. We also show that finding the optimal battery power for convergecast or for broadcast is NP-hard for the class of trees. On the other hand, we give a polynomial algorithm that finds a 2-approximation for convergecast and a 4-approximation for broadcast, for arbitrary graphs.In the distributed setting, we give a 2-competitive algorithm for convergecast in trees and a 4-competitive algorithm for broadcast in trees. The competitive ratio of 2 is proved to be the best for the problem of convergecast, even if we only consider line networks. Indeed, we show that there is no ( @math 2-∈)-competitive algorithm for convergecast or for broadcast in the class of lines, for any @math ∈>0.
In many applications the involved mobile agents are small and have to be produced at low cost in massive numbers. Consequently, in many papers, the computational power of mobile agents is assumed to be very limited and feasibility of some important distributed tasks for such collections of agents is investigated. For example @cite_8 introduced population protocols , modeling wireless sensor networks by extremely limited finite-state computational devices. The agents of population protocols move according to some mobility pattern totally out of their control and they interact randomly in pairs. This is called passive mobility , intended to model, e.g., some unstable environment, like a flow of water, chemical solution, human blood, wind or unpredictable mobility of agents' carriers (e.g. vehicles or flocks of birds). On the other hand, @cite_32 introduced anonymous, oblivious, asynchronous, mobile agents which cannot directly communicate, but they can occasionally observe the environment. Gathering and convergence @cite_17 @cite_33 @cite_10 @cite_34 , as well as pattern formation @cite_18 @cite_37 @cite_32 @cite_36 were studied for such agents.
@cite_18 @cite_37 @cite_33 @cite_8 @cite_36 @cite_32 @cite_34 @cite_10 @cite_17
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Mobile agent computing is being used in fields as diverse as artificial intelligence, computational economics and robotics. Agents' ability to adapt dynamically and execute asynchronously and autonomously brings potential advantages in terms of fault-tolerance, flexibility and simplicity. This monograph focuses on studying mobile agents as modelled in distributed systems research and in particular within the framework of research performed in the distributed algorithms community. It studies the fundamental question of how to achieve rendezvous , the gathering of two or more agents at the same node of a network. Like leader election, such an operation is a useful subroutine in more general computations that may require the agents to synchronize, share information, divide up chores, etc. The work provides an introduction to the algorithmic issues raised by the rendezvous problem in the distributed computing setting. For the most part our investigation concentrates on the simplest case of two agents attempting to rendezvous on a ring network. Other situations including multiple agents, faulty nodes and other topologies are also examined. An extensive bibliography provides many pointers to related work not covered in the text. The presentation has a distinctly algorithmic, rigorous, distributed computing flavor and most results should be easily accessible to advanced undergraduate and graduate students in computer science and mathematics departments. Table of Contents: Models for Mobile Agent Computing Deterministic Rendezvous in a Ring Multiple Agent Rendezvous in a Ring Randomized Rendezvous in a Ring Other Models Other Topologies Two mobile agents (robots) with distinct labels have to meet in an arbitrary, possibly infinite, unknown connected graph or in an unknown connected terrain in the plane. Agents are modeled as points, and the route of each of them only depends on its label and on the unknown environment. The actual walk of each agent also depends on an asynchronous adversary that may arbitrarily vary the speed of the agent, stop it, or even move it back and forth, as long as the walk of the agent in each segment of its route is continuous, does not leave it and covers all of it. Meeting in a graph means that both agents must be at the same time in some node or in some point inside an edge of the graph, while meeting in a terrain means that both agents must be at the same time in some point of the terrain. Does there exist a deterministic algorithm that allows any two agents to meet in any unknown environment in spite of this very powerful adversary? We give deterministic rendezvous algorithms for agents starting at arbitrary nodes of any anonymous connected graph (finite or infinite) and for agents starting at any interior points with rational coordinates in any closed region of the plane with path-connected interior. While our algorithms work in a very general setting - agents can, indeed, meet almost everywhere - we show that none of the above few limitations imposed on the environment can be removed. On the other hand, our algorithm also guarantees the following approximate rendezvous for agents starting at arbitrary interior points of a terrain as above: agents will eventually get at an arbitrarily small positive distance from each other. Two anonymous mobile agents (robots) moving in an asynchronous manner have to meet in an infinite grid of dimension δ > 0, starting from two arbitrary positions at distance at most d. Since the problem is clearly infeasible in such general setting, we assume that the grid is embedded in a δ-dimensional Euclidean space and that each agent knows the Cartesian coordinates of its own initial position (but not the one of the other agent). We design an algorithm permitting the agents to meet after traversing a trajectory of length O(dδ polylog d). This bound for the case of 2D-grids subsumes the main result of [12]. The algorithm is almost optimal, since the Ω(dδ) lower bound is straightforward. Further, we apply our rendezvous method to the following network design problem. The ports of the δ-dimensional grid have to be set such that two anonymous agents starting at distance at most d from each other will always meet, moving in an asynchronous manner, after traversing a O(dδ polylog d) length trajectory. We can also apply our method to a version of the geometric rendezvous problem. Two anonymous agents move asynchronously in the δ-dimensional Euclidean space. The agents have the radii of visibility of r1 and r2, respectively. Each agent knows only its own initial position and its own radius of visibility. The agents meet when one agent is visible to the other one. We propose an algorithm designing the trajectory of each agent, so that they always meet after traveling a total distance of O((d r)δ polylog(d r)), where r = min(r1, r2) and for r ≥ 1. We develop a robust plume tracking strategy using mobile sensor networks in three dimensional (3D) fields. Inspired by the plume tracking behavior of blue crabs, we propose a stochastic model of plume spikes detected by sensing agents based on the Poisson counting process, which enables us to transform the turbulent plume field detected by sensing agents to a continuously-differential field, the minimum of which is considered as a source in the field, and shares the same location with the plume source. The transformation allows us to design and analyze source-seeking algorithms in smooth fields instead of in turbulent fields with higher fluctuation spatially and temporally. Inspired by fish schools that seek darker (shaded) regions in environments with complex lighting variations, we develop a distributed source-seeking algorithm using mobile sensor networks without explicit gradient estimation. The velocity of each agent is designed using only the measurements taken by the agent and the relative positions to its neighboring agents. We prove that, using this design, the moving direction of a three-agent group will converge to the opposite gradient direction of the field, thus, the group moves towards a source in the field. We also prove that the tracking system is input-to-state stable (ISS), indicating that the system is robust to disturbances. We then generalize the design to N-agent groups, and demonstrate the strategy in both smooth fields and turbulent fields in simulations.