{"date_updated":"2021-01-12T08:02:09Z","page":"24","month":"11","pubrep_id":"314","date_created":"2018-12-12T11:39:16Z","alternative_title":["IST Austria Technical Report"],"department":[{"_id":"KrCh"}],"title":"Optimal tree-decomposition balancing and reachability on low treewidth graphs","_id":"5427","publication_identifier":{"issn":["2664-1690"]},"date_published":"2014-11-05T00:00:00Z","ddc":["000"],"author":[{"orcid":"0000-0002-4561-241X","full_name":"Chatterjee, Krishnendu","last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","first_name":"Krishnendu"},{"full_name":"Ibsen-Jensen, Rasmus","last_name":"Ibsen-Jensen","id":"3B699956-F248-11E8-B48F-1D18A9856A87","first_name":"Rasmus","orcid":"0000-0003-4783-0389"},{"orcid":"0000-0002-8943-0722","id":"49704004-F248-11E8-B48F-1D18A9856A87","first_name":"Andreas","full_name":"Pavlogiannis, Andreas","last_name":"Pavlogiannis"}],"status":"public","type":"technical_report","year":"2014","day":"05","citation":{"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>.","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>","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.","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>","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>."},"publication_status":"published","oa":1,"oa_version":"Published Version","doi":"10.15479/AT:IST-2014-314-v1-1","file_date_updated":"2020-07-14T12:46:52Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"relation":"main_file","file_id":"5471","file_name":"IST-2014-314-v1+1_long.pdf","content_type":"application/pdf","date_created":"2018-12-12T11:53:10Z","creator":"system","date_updated":"2020-07-14T12:46:52Z","access_level":"open_access","file_size":405561,"checksum":"9d3b90bf4fff74664f182f2d95ef727a"}],"language":[{"iso":"eng"}],"has_accepted_license":"1","publisher":"IST Austria","abstract":[{"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.","lang":"eng"}]}