Cost vs. Information Tradeoffs for Treasure Hunt in the Plane
Andrzej Pelc, Ram Narayan Yadav

TL;DR
This paper explores the relationship between the amount of prior information and the cost of a treasure hunt in the plane, proposing algorithms that adapt to different advice sizes and vision radii.
Contribution
It introduces advice-based algorithms that achieve near-optimal or almost optimal costs depending on the vision radius relative to the distance.
Findings
Algorithms are optimal for small or large vision radii.
For intermediate radii, algorithms are nearly optimal with a small overhead.
Advice size directly influences the efficiency of treasure hunt algorithms.
Abstract
A mobile agent has to find an inert treasure hidden in the plane. Both the agent and the treasure are modeled as points. This is a variant of the task known as treasure hunt. The treasure is at a distance at most from the initial position of the agent, and the agent finds the treasure when it gets at distance from it, called the {\em vision radius}. However, the agent does not know the location of the treasure and does not know the parameters and . The cost of finding the treasure is the length of the trajectory of the agent. We investigate the tradeoffs between the amount of information held {\em a priori} by the agent and the cost of treasure hunt. Following the well-established paradigm of {\em algorithms with advice}, this information is given to the agent in advance as a binary string, by an oracle cooperating with the agent and knowing the location of the treasure…
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Taxonomy
TopicsOptimization and Search Problems · Complexity and Algorithms in Graphs · Auction Theory and Applications
