{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T06:32:25Z","timestamp":1759991545445,"version":"3.41.0"},"reference-count":28,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2023,5,5]],"date-time":"2023-05-05T00:00:00Z","timestamp":1683244800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"NSERC discovery grant","award":["2018-03899"],"award-info":[{"award-number":["2018-03899"]}]},{"name":"Research Chair in Distributed Computing of the Universit\u00e9 du Qu\u00e9bec en Outaouais"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Algorithms"],"published-print":{"date-parts":[[2023,7,31]]},"abstract":"<jats:p>\n            A mobile agent navigating along edges of a simple connected unweighted graph, either finite or countably infinite, has to find an inert target (treasure) hidden in one of the nodes. This task is known as treasure hunt. The agent has no\n            <jats:italic>a priori<\/jats:italic>\n            knowledge of the graph, of the location of the treasure, or of the initial distance to it. The cost of a treasure hunt algorithm is the worst-case number of edge traversals performed by the agent until finding the treasure. Awerbuch et\u00a0al. [\n            <jats:xref ref-type=\"bibr\">3<\/jats:xref>\n            ] considered graph exploration and treasure hunt for finite graphs in a restricted model where the agent has a fuel tank that can be replenished only at the starting node\n            <jats:italic>s<\/jats:italic>\n            . The size of the tank is\n            <jats:italic>B = 2 (1+\u03b1) r<\/jats:italic>\n            , for some positive real constant \u03b1, where\n            <jats:italic>r<\/jats:italic>\n            , called the radius of the graph, is the maximum distance from\n            <jats:italic>s<\/jats:italic>\n            to any other node. The tank of size\n            <jats:italic>B<\/jats:italic>\n            allows the agent to make at most \u230a B \u230b edge traversals between two consecutive visits at node\n            <jats:italic>s<\/jats:italic>\n            .\n          <\/jats:p>\n          <jats:p>\n            Let\n            <jats:italic>e(d)<\/jats:italic>\n            be the number of edges whose at least one endpoint is at distance less than\n            <jats:italic>d<\/jats:italic>\n            from\n            <jats:italic>s<\/jats:italic>\n            . Awerbuch et\u00a0al. [\n            <jats:xref ref-type=\"bibr\">3<\/jats:xref>\n            ] conjectured that it is impossible to find a treasure hidden in a node at distance at most\n            <jats:italic>d<\/jats:italic>\n            at cost nearly linear in\n            <jats:italic>e(d)<\/jats:italic>\n            . We first design a deterministic treasure hunt algorithm working in the model without any restrictions on the moves of the agent at cost\n            <jats:italic>\ud835\udcaa(e(d)<\/jats:italic>\n            log\n            <jats:italic>d<\/jats:italic>\n            ) and then show how to modify this algorithm to work in the model from Awerbuch et\u00a0al. [\n            <jats:xref ref-type=\"bibr\">3<\/jats:xref>\n            ] with the same complexity. Thus, we refute the preceding 20-year-old conjecture. We observe that no treasure hunt algorithm can beat cost \u0398 (\n            <jats:italic>e(d)<\/jats:italic>\n            ) for all graphs, and thus our algorithms are also almost optimal.\n          <\/jats:p>","DOI":"10.1145\/3588437","type":"journal-article","created":{"date-parts":[[2023,3,18]],"date-time":"2023-03-18T10:11:45Z","timestamp":1679134305000},"page":"1-32","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Almost-Optimal Deterministic Treasure Hunt in Unweighted Graphs"],"prefix":"10.1145","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6464-9517","authenticated-orcid":false,"given":"S\u00e9bastien","family":"Bouchard","sequence":"first","affiliation":[{"name":"Universit\u00e9 de Bordeaux, Bordeaux INP, CNRS, LaBRI, Bordeaux, 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