Deterministic Searching on the Line
Keywords and Synonyms
Searching for a point in a line; Searching in one dimension; Searching for a line (or a plane) of known slope in the plane (or a 3D space)
The problem is to design a strategy for a searcher (or a number of searchers) located initially at some start point on a line to reach an unknown target point. The target point is detected only when a searcher is located on it. There are several variations depending on the information about the target point, how many parallel searchers are available and how they can communicate, and the type of algorithm. The cost of the search algorithm is defined as the distance traveled until finding the point relative to the distance of the starting point to the target. This entry only covers deterministic algorithms.
Consider just one searcher. If one knows the direction to the target, the solution is trivial and the relative cost is 1. If one knows the distance to the target, the solution is also simple....
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