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.
Assumptions similar to our paper have been made in @cite_19 @cite_0 @cite_29 where the mobile agents are constrained to travel a fixed distance to explore an unknown graph @cite_19 @cite_0 , or tree @cite_29 . In @cite_19 @cite_0 a mobile agent has to return to its home base to refuel (or recharge its battery) so that the same maximal distance may repeatedly be traversed. @cite_29 gives an 8-competitive distributed algorithm for a set of agents with the same amount of power exploring the tree starting at the same node.
@cite_0 @cite_19 @cite_29
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Consider a robot that has to travel from a start location @math to a target @math in an environment with opaque obstacles that lie in its way. The robot always knows its current absolute position and that of the target. It does not, however, know the positions and extents of the obstacles in advance; rather, it finds out about obstacles as it encounters them. We compare the distance walked by the robot in going from @math to @math to the length of the shortest (obstacle-free) path between @math and @math in the scene. We describe and analyze robot strategies that minimize this ratio for different kinds of scenes. In particular, we consider the cases of rectangular obstacles aligned with the axes, rectangular obstacles in more general orientations, and wider classes of convex bodies both in two and three dimensions. For many of these situations, our algorithms are optimal up to constant factors. We study scenes with nonconvex obstacles, which are related to the study of maze traversal. We also show scenes where randomized algorithms are provably better than deterministic algorithms. We study how a mobile robot can learn an unknown environment in a piecemeal manner. The robot's goal is to learn a complete map of its environment, while satisfying the constraint that it must return every so often to its starting position (for refueling, say). The environment is modeled as an arbitrary, undirected graph, which is initially unknown to the robot. We assume that the robot can distinguish vertices and edges that it has already explored. We present a surprisingly efficient algorithm for piecemeal learning an unknown undirected graph G=(V, E) in which the robot explores every vertex and edge in the graph by traversing at most O(E+V1+o(1)) edges. This nearly linear algorithm improves on the best previous algorithm, in which the robot traverses at most O(E+V2) edges. We also give an application of piecemeal learning to the problem of searching a graph for a “treasure.”