{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article11900","name":"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 optimal. 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(D^{2-epsilon}), 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 Theta(D^2) cannot be beaten.","keywords":["treasure hunt","deterministic algorithm","mobile agent","hint","plane"],"author":[{"@type":"Person","name":"Bouchard, S\u00e9bastien","givenName":"S\u00e9bastien","familyName":"Bouchard","affiliation":"Sorbonne Universit\u00e9, CNRS, INRIA, LIP6, F-75005 Paris, France"},{"@type":"Person","name":"Dieudonn\u00e9, Yoann","givenName":"Yoann","familyName":"Dieudonn\u00e9","affiliation":"Laboratoire MIS, Universit\u00e9 de Picardie Jules Verne, Amiens, France"},{"@type":"Person","name":"Pelc, Andrzej","givenName":"Andrzej","familyName":"Pelc","affiliation":"D\u00e9partement d'informatique, Universit\u00e9 du Qu\u00e9bec en Outaouais, Gatineau, Canada","funding":"This work was supported in part by NSERC discovery grant 8136 - 2013 and by the Research Chair in Distributed Computing of the Universit\u00e9 du Qu\u00e9bec en Outaouais."},{"@type":"Person","name":"Petit, Franck","givenName":"Franck","familyName":"Petit","affiliation":"Sorbonne Universit\u00e9, CNRS, INRIA, LIP6, F-75005 Paris, France","funding":"This work was performed within Project ESTATE (Ref. ANR-16-CE25-0009-03), supported by French state funds managed by the ANR (Agence Nationale de la Recherche)."}],"position":48,"pageStart":"48:1","pageEnd":"48:13","dateCreated":"2018-12-06","datePublished":"2018-12-06","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Bouchard, S\u00e9bastien","givenName":"S\u00e9bastien","familyName":"Bouchard","affiliation":"Sorbonne Universit\u00e9, CNRS, INRIA, LIP6, F-75005 Paris, France"},{"@type":"Person","name":"Dieudonn\u00e9, Yoann","givenName":"Yoann","familyName":"Dieudonn\u00e9","affiliation":"Laboratoire MIS, Universit\u00e9 de Picardie Jules Verne, Amiens, France"},{"@type":"Person","name":"Pelc, Andrzej","givenName":"Andrzej","familyName":"Pelc","affiliation":"D\u00e9partement d'informatique, Universit\u00e9 du Qu\u00e9bec en Outaouais, Gatineau, Canada","funding":"This work was supported in part by NSERC discovery grant 8136 - 2013 and by the Research Chair in Distributed Computing of the Universit\u00e9 du Qu\u00e9bec en Outaouais."},{"@type":"Person","name":"Petit, Franck","givenName":"Franck","familyName":"Petit","affiliation":"Sorbonne Universit\u00e9, CNRS, INRIA, LIP6, F-75005 Paris, France","funding":"This work was performed within Project ESTATE (Ref. ANR-16-CE25-0009-03), supported by French state funds managed by the ANR (Agence Nationale de la Recherche)."}],"copyrightYear":"2018","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.ISAAC.2018.48","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume6326","volumeNumber":123,"name":"29th International Symposium on Algorithms and Computation (ISAAC 2018)","dateCreated":"2018-12-06","datePublished":"2018-12-06","editor":[{"@type":"Person","name":"Hsu, Wen-Lian","givenName":"Wen-Lian","familyName":"Hsu"},{"@type":"Person","name":"Lee, Der-Tsai","givenName":"Der-Tsai","familyName":"Lee"},{"@type":"Person","name":"Liao, Chung-Shou","givenName":"Chung-Shou","familyName":"Liao"}],"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article11900","isPartOf":{"@type":"Periodical","@id":"#series116","name":"Leibniz International Proceedings in Informatics","issn":"1868-8969","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume6326"}}}