{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T04:36:54Z","timestamp":1759639014939,"version":"3.41.0"},"reference-count":25,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2017,12,5]],"date-time":"2017-12-05T00:00:00Z","timestamp":1512432000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Comput. Theory"],"published-print":{"date-parts":[[2017,12,31]]},"abstract":"<jats:p>\n            Given a graph\n            <jats:italic>G<\/jats:italic>\n            and two vertices\n            <jats:italic>s<\/jats:italic>\n            and\n            <jats:italic>t<\/jats:italic>\n            in it,\n            <jats:italic>graph reachability<\/jats:italic>\n            is the problem of checking whether there exists a path from\n            <jats:italic>s<\/jats:italic>\n            to\n            <jats:italic>t<\/jats:italic>\n            in\n            <jats:italic>G<\/jats:italic>\n            . We show that reachability in directed layered planar graphs can be decided in polynomial time and\n            <jats:italic>O<\/jats:italic>\n            (\n            <jats:italic>n<\/jats:italic>\n            <jats:sup>\u03f5<\/jats:sup>\n            ) space, for any \u03f5 &gt; 0. The previous best-known space bound for this problem with polynomial time was approximately\n            <jats:italic>O<\/jats:italic>\n            (\u221a\n            <jats:italic>n<\/jats:italic>\n            ) space (Imai et al. 2013).\n          <\/jats:p>\n          <jats:p>Deciding graph reachability in SC (Steve's class) is an important open question in complexity theory, and in this article, we make progress toward resolving this question.<\/jats:p>","DOI":"10.1145\/3154857","type":"journal-article","created":{"date-parts":[[2017,12,6]],"date-time":"2017-12-06T21:23:15Z","timestamp":1512595395000},"page":"1-11","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["An\n            <i>O<\/i>\n            (\n            <i>n<\/i>\n            <sup>\u03f5<\/sup>\n            ) Space and Polynomial Time Algorithm for Reachability in Directed Layered Planar Graphs"],"prefix":"10.1145","volume":"9","author":[{"given":"Diptarka","family":"Chakraborty","sequence":"first","affiliation":[{"name":"Computer Science Institute of Charles University, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Raghunath","family":"Tewari","sequence":"additional","affiliation":[{"name":"Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2017,12,5]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-73001-9_3"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00224-009-9172-z"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/s002240000102"},{"volume-title":"Computational Complexity - A Modern Approach","author":"Arora Sanjeev","key":"e_1_2_1_4_1","unstructured":"Sanjeev Arora and Boaz Barak . 2009. 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Kirkpatrick , Kotaro Nakagawa , and Osamu Watanabe . 2014 . \u00d5(&radic;n)-Space and polynomial-time algorithm for planar directed graph reachability . In Proceedings of the 39th International Symposium on Mathematical Foundations of Computer Science 2014, Part II, MFCS 2014 , Budapest, Hungary , August 25-29, 2014. 45--56. Tetsuo Asano, David G. Kirkpatrick, Kotaro Nakagawa, and Osamu Watanabe. 2014. \u00d5(&radic;n)-Space and polynomial-time algorithm for planar directed graph reachability. 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