We introduce a new geometric routing problem which arises in data muling applications where a mobile robot is charged with collecting data from stationary sensors. The objective is to compute the robot's trajectory and download sequence so as to minimize the time to collect the data from all sensors. The total data collection time has two components: the robot's travel time and the download time. The time to download data from a sensor s is a function of the locations of the robot and s: If the robot is a distance rinβ away from s, it can download the sensor's data in Tinβ units of time. If the distance is greater than rinβ but less than routβ, the download time is T_{out} > T_{in}. Otherwise, the robot can not download the data from s. Here, rinβ, routβ, Tinβ and Toutβ are input parameters. We refer to this model, which is based on recently developed experimental models for sensor network deployments, as the two ring model, and the problem of downloading data from a given set of sensors in minimum amount of time under this model as the Two-Ring Tour (TRT) problem.
We present approximation algorithms for the general case which uses solutions to the Traveling Salesperson with Neighborhoods (TSPN) Problem as subroutines. We also present efficient solutions to special but practically important versions of the problem such as uniform and sparse deployment