{"doi":"10.15479/AT:IST-2014-187-v1-1","title":"Improved algorithms for reachability and shortest path on low tree-width graphs","publisher":"IST Austria","pubrep_id":"187","publication_status":"published","day":"14","author":[{"full_name":"Chatterjee, Krishnendu","first_name":"Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","orcid":"0000-0002-4561-241X"},{"orcid":"0000-0003-4783-0389","last_name":"Ibsen-Jensen","id":"3B699956-F248-11E8-B48F-1D18A9856A87","first_name":"Rasmus","full_name":"Ibsen-Jensen, Rasmus"},{"first_name":"Andreas","full_name":"Pavlogiannis, Andreas","last_name":"Pavlogiannis","orcid":"0000-0002-8943-0722","id":"49704004-F248-11E8-B48F-1D18A9856A87"}],"date_updated":"2021-01-12T08:02:03Z","file_date_updated":"2020-07-14T12:46:50Z","_id":"5419","abstract":[{"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.","lang":"eng"}],"oa":1,"language":[{"iso":"eng"}],"date_published":"2014-04-14T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2018-12-12T11:39:13Z","file":[{"file_name":"IST-2014-187-v1+1_main_full_tech.pdf","access_level":"open_access","date_updated":"2020-07-14T12:46:50Z","relation":"main_file","creator":"system","file_size":670031,"content_type":"application/pdf","checksum":"c608e66030a4bf51d2d99b451f539b99","date_created":"2018-12-12T11:54:25Z","file_id":"5548"}],"alternative_title":["IST Austria Technical Report"],"year":"2014","page":"34","oa_version":"Published Version","citation":{"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.","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>.","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>","ista":"Chatterjee K, Ibsen-Jensen R, Pavlogiannis A. 2014. Improved algorithms for reachability and shortest path on low tree-width graphs, IST Austria, 34p.","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.","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>."},"status":"public","department":[{"_id":"KrCh"}],"type":"technical_report","ddc":["000"],"month":"04","has_accepted_license":"1","publication_identifier":{"issn":["2664-1690"]}}