Keywords and Synonyms
Cow-path problem ; On-line navigation
Problem Definition
This problem deals with finding a point at an unknown position on one of a set of w rays which extend from a common point (the origin). In this problem there is a searcher, who starts at the origin, and follows a sequence of commands such as “explore to distance d on ray i.” The searcher detects immdiately when the target point is crossed, but there is no other information provided from the search environment. The goal of the searcher is to minimize the distance traveled.
There are several different ways this problem has been formulated in the literature, including one called the “cow-path problem” that involves a cow searching for a pasture down a set of paths. When \( { w=2 } \), this problem is to search for a point on the line, which has also been described as a robot searching for a door in an infinite wall or a shipwreck survivor searching for a stream after washing ashore on a beach.
Notation
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Recommended Reading
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Tate, S. (2008). Randomized Searching on Rays or the Line. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_328
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