{"alternative_title":["IST Austria Technical Report"],"title":"Improved algorithms for reachability and shortest path on low tree-width graphs","_id":"5419","author":[{"last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","full_name":"Chatterjee, Krishnendu","first_name":"Krishnendu","orcid":"0000-0002-4561-241X"},{"id":"3B699956-F248-11E8-B48F-1D18A9856A87","last_name":"Ibsen-Jensen","orcid":"0000-0003-4783-0389","full_name":"Ibsen-Jensen, Rasmus","first_name":"Rasmus"},{"last_name":"Pavlogiannis","id":"49704004-F248-11E8-B48F-1D18A9856A87","full_name":"Pavlogiannis, Andreas","first_name":"Andreas","orcid":"0000-0002-8943-0722"}],"doi":"10.15479/AT:IST-2014-187-v1-1","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We consider the reachability and shortest path problems on low tree-width graphs, with n nodes, m edges, and tree-width t, on a standard RAM with wordsize W. We use O to hide polynomial factors of the inverse of the Ackermann function. Our main contributions are three fold:\r\n1. For reachability, we present an algorithm that requires O(n·t2·log(n/t)) preprocessing time, O(n·(t·log(n/t))/W) space, and O(t/W) time for pair queries and O((n·t)/W) time for single-source queries. Note that for constant t our algorithm uses O(n·logn) time for preprocessing; and O(n/W) time for single-source queries, which is faster than depth first search/breath first search (after the preprocessing).\r\n2. We present an algorithm for shortest path that requires O(n·t2) preprocessing time, O(n·t) space, and O(t2) time for pair queries and O(n·t) time single-source queries.\r\n3. We give a space versus query time trade-off algorithm for shortest path that, given any constant >0, requires O(n·t2) preprocessing time, O(n·t2) space, and O(n1−·t2) time for pair queries.\r\nOur algorithms improve all existing results, and use very simple data structures."}],"publication_status":"published","type":"technical_report","has_accepted_license":"1","date_updated":"2021-01-12T08:02:03Z","language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","file_size":670031,"access_level":"open_access","file_name":"IST-2014-187-v1+1_main_full_tech.pdf","relation":"main_file","date_created":"2018-12-12T11:54:25Z","checksum":"c608e66030a4bf51d2d99b451f539b99","creator":"system","file_id":"5548","date_updated":"2020-07-14T12:46:50Z"}],"publication_identifier":{"issn":["2664-1690"]},"pubrep_id":"187","day":"14","year":"2014","status":"public","publisher":"IST Austria","page":"34","oa":1,"file_date_updated":"2020-07-14T12:46:50Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2014-04-14T00:00:00Z","ddc":["000"],"department":[{"_id":"KrCh"}],"month":"04","date_created":"2018-12-12T11:39:13Z","citation":{"ista":"Chatterjee K, Ibsen-Jensen R, Pavlogiannis A. 2014. Improved algorithms for reachability and shortest path on low tree-width graphs, IST Austria, 34p.","chicago":"Chatterjee, Krishnendu, Rasmus Ibsen-Jensen, and Andreas Pavlogiannis. <i>Improved Algorithms for Reachability and Shortest Path on Low Tree-Width Graphs</i>. IST Austria, 2014. <a href=\"https://doi.org/10.15479/AT:IST-2014-187-v1-1\">https://doi.org/10.15479/AT:IST-2014-187-v1-1</a>.","apa":"Chatterjee, K., Ibsen-Jensen, R., &#38; Pavlogiannis, A. (2014). <i>Improved algorithms for reachability and shortest path on low tree-width graphs</i>. IST Austria. <a href=\"https://doi.org/10.15479/AT:IST-2014-187-v1-1\">https://doi.org/10.15479/AT:IST-2014-187-v1-1</a>","short":"K. Chatterjee, R. Ibsen-Jensen, A. Pavlogiannis, Improved Algorithms for Reachability and Shortest Path on Low Tree-Width Graphs, IST Austria, 2014.","ama":"Chatterjee K, Ibsen-Jensen R, Pavlogiannis A. <i>Improved Algorithms for Reachability and Shortest Path on Low Tree-Width Graphs</i>. IST Austria; 2014. doi:<a href=\"https://doi.org/10.15479/AT:IST-2014-187-v1-1\">10.15479/AT:IST-2014-187-v1-1</a>","mla":"Chatterjee, Krishnendu, et al. <i>Improved Algorithms for Reachability and Shortest Path on Low Tree-Width Graphs</i>. IST Austria, 2014, doi:<a href=\"https://doi.org/10.15479/AT:IST-2014-187-v1-1\">10.15479/AT:IST-2014-187-v1-1</a>.","ieee":"K. Chatterjee, R. Ibsen-Jensen, and A. Pavlogiannis, <i>Improved algorithms for reachability and shortest path on low tree-width graphs</i>. IST Austria, 2014."}}