Can Walker Localize The Middle Point of A Line-segment?
Abstract
This paper poses a question about a simple localization problem. The question is if an oblivious walker on a line-segment can localize the middle point of the line-segment in finite steps observing the direction (i.e., Left or Right) and the distance to the nearest end point. This problem is arisen from self-stabilizing location problems by autonomous mobile robots with limited visibility, that is a widely interested abstract model in distributed computing. Contrary to appearances, it is far from trivial if this simple problem is solvable or not, and unsettled yet. This paper is concerned with three variants of the problem with a minimal relaxation, and presents self-stabilizing algorithms for them. We also show an easy impossibility theorem for bilaterally symmetric algorithms.
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.