{"language":[{"iso":"eng"}],"pubrep_id":"314","file":[{"date_updated":"2020-07-14T12:46:52Z","file_id":"5471","creator":"system","relation":"main_file","file_name":"IST-2014-314-v1+1_long.pdf","access_level":"open_access","checksum":"9d3b90bf4fff74664f182f2d95ef727a","date_created":"2018-12-12T11:53:10Z","file_size":405561,"content_type":"application/pdf"}],"publication_identifier":{"issn":["2664-1690"]},"has_accepted_license":"1","type":"technical_report","date_updated":"2021-01-12T08:02:09Z","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We consider graphs with n nodes together with their tree-decomposition that has b = O ( n ) bags and width t , on the standard RAM computational model with wordsize W = Θ (log n ) . Our contributions are two-fold: Our first contribution is an algorithm that given a graph and its tree-decomposition as input, computes a binary and balanced tree-decomposition of width at most 4 · t + 3 of the graph in O ( b ) time and space, improving a long-standing (from 1992) bound of O ( n · log n ) time for constant treewidth graphs. Our second contribution is on reachability queries for low treewidth graphs. We build on our tree-balancing algorithm and present a data-structure for graph reachability that requires O ( n · t 2 ) preprocessing time, O ( n · t ) space, and O ( d t/ log n e ) time for pair queries, and O ( n · t · log t/ log n ) time for single-source queries. For constant t our data-structure uses O ( n ) time for preprocessing, O (1) time for pair queries, and O ( n/ log n ) time for single-source queries. This is (asymptotically) optimal and is faster than DFS/BFS when answering more than a constant number of single-source queries."}],"publication_status":"published","alternative_title":["IST Austria Technical Report"],"title":"Optimal tree-decomposition balancing and reachability on low treewidth graphs","doi":"10.15479/AT:IST-2014-314-v1-1","author":[{"first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu","orcid":"0000-0002-4561-241X","last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87"},{"id":"3B699956-F248-11E8-B48F-1D18A9856A87","last_name":"Ibsen-Jensen","orcid":"0000-0003-4783-0389","full_name":"Ibsen-Jensen, Rasmus","first_name":"Rasmus"},{"orcid":"0000-0002-8943-0722","first_name":"Andreas","full_name":"Pavlogiannis, Andreas","id":"49704004-F248-11E8-B48F-1D18A9856A87","last_name":"Pavlogiannis"}],"_id":"5427","date_created":"2018-12-12T11:39:16Z","month":"11","citation":{"chicago":"Chatterjee, Krishnendu, Rasmus Ibsen-Jensen, and Andreas Pavlogiannis. <i>Optimal Tree-Decomposition Balancing and Reachability on Low Treewidth Graphs</i>. IST Austria, 2014. <a href=\"https://doi.org/10.15479/AT:IST-2014-314-v1-1\">https://doi.org/10.15479/AT:IST-2014-314-v1-1</a>.","ista":"Chatterjee K, Ibsen-Jensen R, Pavlogiannis A. 2014. Optimal tree-decomposition balancing and reachability on low treewidth graphs, IST Austria, 24p.","apa":"Chatterjee, K., Ibsen-Jensen, R., &#38; Pavlogiannis, A. (2014). <i>Optimal tree-decomposition balancing and reachability on low treewidth graphs</i>. IST Austria. <a href=\"https://doi.org/10.15479/AT:IST-2014-314-v1-1\">https://doi.org/10.15479/AT:IST-2014-314-v1-1</a>","ama":"Chatterjee K, Ibsen-Jensen R, Pavlogiannis A. <i>Optimal Tree-Decomposition Balancing and Reachability on Low Treewidth Graphs</i>. IST Austria; 2014. doi:<a href=\"https://doi.org/10.15479/AT:IST-2014-314-v1-1\">10.15479/AT:IST-2014-314-v1-1</a>","mla":"Chatterjee, Krishnendu, et al. <i>Optimal Tree-Decomposition Balancing and Reachability on Low Treewidth Graphs</i>. IST Austria, 2014, doi:<a href=\"https://doi.org/10.15479/AT:IST-2014-314-v1-1\">10.15479/AT:IST-2014-314-v1-1</a>.","short":"K. Chatterjee, R. Ibsen-Jensen, A. Pavlogiannis, Optimal Tree-Decomposition Balancing and Reachability on Low Treewidth Graphs, IST Austria, 2014.","ieee":"K. Chatterjee, R. Ibsen-Jensen, and A. Pavlogiannis, <i>Optimal tree-decomposition balancing and reachability on low treewidth graphs</i>. IST Austria, 2014."},"department":[{"_id":"KrCh"}],"file_date_updated":"2020-07-14T12:46:52Z","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ddc":["000"],"date_published":"2014-11-05T00:00:00Z","day":"05","page":"24","year":"2014","publisher":"IST Austria","status":"public"}