Paper Info
Title
Deterministic Treasure Hunt In The Plane With Angular Hints
Abstract
A mobile agent equipped with a compass and a measure of length has to find an inert treasure in the Euclidean plane. Both the agent and the treasure are modeled as points. In the beginning, the agent is at a distance at most D > 0 from the treasure, but knows neither the distance nor any bound on it. Finding the treasure means getting at distance at most 1 from it. The agent makes a series of moves. Each of them consists in moving straight in a chosen direction at a chosen distance. In the beginning and after each move the agent gets a hint consisting of a positive angle smaller than 2 pi whose vertex is at the current position of the agent and within which the treasure is contained. We investigate the problem of how these hints permit the agent to lower the cost of finding the treasure, using a deterministic algorithm, where the cost is the worst-case total length of the agent's trajectory. It is well known that without any hint the optimal (worst case) cost is Theta(D-2). We show that if all angles given as hints are at most pi, then the cost can be lowered to O(D), which is the optimal complexity. If all angles are at most beta, where beta < 2 pi is a constant unknown to the agent, then the cost is at most O(D2-e), for some epsilon > 0. For both these positive results we present deterministic algorithms achieving the above costs. Finally, if angles given as hints can be arbitrary, smaller than 2 pi, then we show that cost complexity Theta(D-2) cannot be beaten.
Year
DOI
Venue
2020
10.1007/s00453-020-00724-4
ALGORITHMICA
Keywords
DocType
Volume
Exploration, Treasure hunt, Algorithm, Mobile agent, Hint, Cost, Plane
Journal
82
Issue
ISSN
Citations 
11
0178-4617
0
PageRank 
References 
Authors
0.34
0
4
Name
Order
Citations
PageRank
Sébastien Bouchard102.70
Yoann Dieudonné222119.88
Andrzej Pelc33416246.55
Franck Petit473660.02