Online Search with a Hint
The linear search problem, informally known as the cow path problem, is one of the fundamental problems in search theory. In this problem, an immobile target is hidden at some unknown position on an unbounded line, and a mobile searcher, initially positioned at some specific point of the line called the root, must traverse the line so as to locate the target. The objective is to minimize the worst-case ratio of the distance traversed by the searcher to the distance of the target from the root, which is known as the competitive ratio of the search.
In this work we study this problem in a setting in which the searcher has a hint concerning the target. We consider three settings in regards to the nature of the hint: i) the hint suggests the exact position of the target on the line; ii) the hint suggests the direction of the optimal search (i.e., to the left or the right of the root); and iii) the hint is a general k-bit string that encodes some information concerning the target. Our objective is to study the Pareto-efficiency of strategies in this model. Namely, we seek optimal, or near-optimal tradeoffs between the searcher’s performance if the hint is correct (i.e., provided by a trusted source) and if the hint is incorrect (i.e., provided by an adversary).
Search problems
searching on the line
competitive analysis
predictions
Theory of computation~Online algorithms
51:1-51:16
Regular Paper
A full version of this paper is available at https://arxiv.org/pdf/2008.13729.pdf.
I am thankful to Thomas Lidbetter for his comments on an early version of this paper.
Spyros
Angelopoulos
Spyros Angelopoulos
Sorbonne Université, CNRS, Laboratoire d’informatique de Paris 6, LIP6, 75252 Paris, France
http://lip6.fr/Spyros.Angelopoulos
https://orcid.org/0000-0001-9819-9158
Research benefited from the support of the FMJH Program PGMO and from the support to this program from EDF-THALES-ORANGE. Also partially funded by the grant ANR-19-CE48-0016 from the French National Research Agency (ANR).
10.4230/LIPIcs.ITCS.2021.51
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Spyros Angelopoulos
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