{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,5]],"date-time":"2024-08-05T17:08:41Z","timestamp":1722877721202},"reference-count":33,"publisher":"Association for Computing Machinery (ACM)","issue":"6","content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["J. ACM"],"published-print":{"date-parts":[[2004,11]]},"abstract":"\n It is shown that a planar digraph can be preprocessed in near-linear time, producing a near-linear space oracle that can answer reachability queries in constant time. The oracle can be distributed as an\n O<\/jats:italic>\n (log\n n<\/jats:italic>\n ) space label for each vertex and then we can determine if one vertex can reach another considering their two labels only.The approach generalizes to give a near-linear space approximate distances oracle for a weighted planar digraph. With weights drawn from {0, \u2026,\n N<\/jats:italic>\n }, it approximates distances within a factor (1 + \u03b5) in\n O<\/jats:italic>\n (log log (\n nN<\/jats:italic>\n ) + 1\/\u03b5) time. Our scheme can be extended to find and route along correspondingly short dipaths.\n <\/jats:p>","DOI":"10.1145\/1039488.1039493","type":"journal-article","created":{"date-parts":[[2005,1,26]],"date-time":"2005-01-26T16:35:53Z","timestamp":1106757353000},"page":"993-1024","update-policy":"http:\/\/dx.doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":151,"title":["Compact oracles for reachability and approximate distances in planar digraphs"],"prefix":"10.1145","volume":"51","author":[{"given":"Mikkel","family":"Thorup","sequence":"first","affiliation":[{"name":"AT&T Labs---Research, Florham Park, New Jersey"}]}],"member":"320","published-online":{"date-parts":[[2004,11]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"Proceedings of the 4th European Symposium on Algorithms","volume":"1136","author":"Arikati S."},{"key":"e_1_2_1_2_1","volume-title":"Proceedings of the 6th Annual ACM-SIAM Symposium on Discrete Algorithms","author":"Chen D.","year":"1995"},{"key":"e_1_2_1_3_1","volume-title":"Proceedings of the 32nd Annual ACM Symposium on Theory of Computing (Portland, Ore.). 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