Maintaining Privacy on a Line

Consider a situation where people have to choose among a sequence of n linearly ordered positions to perform some task requiring a certain amount of privacy. Which position should one choose so as to maximize one’s privacy, i.e., minimize the chances that one of your neighboring positions becomes occupied by a later arrival? In this paper, we attempt to answer this question under a variety of models for the behavior of the later arrivals. Our results suggest that for the most part one should probably choose one of the extreme positions (with some interesting exceptions). We also suggest a number of variations on the problem that lead to many open problems.