Online Search With a Hint

TL;DR

This paper explores the linear search problem with hints, analyzing how different types of hints affect the searcher's efficiency and the tradeoffs between correct and adversarial hints.

Contribution

It introduces a new model of the cow path problem incorporating various hint types and studies the Pareto-efficiency of strategies balancing performance with correct and incorrect hints.

Findings

Optimal strategies depend on hint accuracy and type.

Tradeoffs between performance with trusted and adversarial hints are characterized.

The model extends classical search theory with information hints.

Abstract

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).