Going Far, Logically

There are numerous applications where we need to ensure that multiple moving objects are sufficiently far apart. Furthermore, in many moving object domains, there is positional indeterminacy - we are not 100% sure exactly when a given moving object will be at a given location. [Yaman et al., 2004] provided a logic of motion but did not provide algorithms to ensure that moving objects are kept sufficiently far apart. In this paper, we extend their logic to include a "far" predicate. We develop the CheckFar algorithm that checks if any given two objects will always be sufficiently far apart at during a time interval. We have run a set of experiments showing that our CheckFar algorithm scales very well.