Reference Work Entry

Encyclopedia of Algorithms

pp 531-533


Deterministic Searching on the Line

  • Spyros AngelopoulosAffiliated withSorbonne Universités, L’Université Pierre et Marie Curie (UPMC), Université Paris 06 Email author 


Online Searching Pure strategies Searching for a point on the infinite line Searching in one dimension

Years and Authors of Summarized Original Work

  • 1993; Baeza-Yates, Culberson, Rawlins

  • 2001; Jaillet, Stafford

Problem Definition

In the Linear Search Problem (LSP), we seek efficient strategies for locating an immobile target on the infinite line. More formally, the search environment consists of the infinite (i.e., unbounded) line, with a point O designated as a specific start point. A mobile searcher is initially located at O, whereas the target may be hidden at any point on the line. The searcher’s strategy S defines the movement of the searcher on the line; on the other hand, the hider’s strategy H is defined as the precise placement of the target on the line, and we denote by | H | the distance of the target from the start point. Given strategies S, H, the cost of locating the target, denoted by c(S, H) is the total distance traversed by the searcher at the first time the target is located. The normalized cost of the strategies is defined as the quantity ...

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