{"month":"01","publication_status":"published","language":[{"iso":"eng"}],"quality_controlled":"1","acknowledgement":"This work was begun at the University of Waterloo and was partially supported by the Natural Sciences and Engineering Council of Canada (NSERC).\r\n","publisher":"EPI Sciences","date_created":"2023-04-16T22:01:08Z","has_accepted_license":"1","file":[{"date_updated":"2023-04-17T08:10:28Z","date_created":"2023-04-17T08:10:28Z","access_level":"open_access","content_type":"application/pdf","file_id":"12844","file_size":2072197,"success":1,"file_name":"2022_DMTCS_Biniaz.pdf","creator":"dernst","checksum":"439102ea4f6e2aeefd7107dfb9ccf532","relation":"main_file"}],"ddc":["000"],"title":"Token swapping on trees","article_number":"9","year":"2023","related_material":{"record":[{"id":"7950","status":"public","relation":"earlier_version"}]},"file_date_updated":"2023-04-17T08:10:28Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"citation":{"short":"A. Biniaz, K. Jain, A. Lubiw, Z. Masárová, T. Miltzow, D. Mondal, A.M. Naredla, J. Tkadlec, A. Turcotte, Discrete Mathematics and Theoretical Computer Science 24 (2023).","ama":"Biniaz A, Jain K, Lubiw A, et al. Token swapping on trees. <i>Discrete Mathematics and Theoretical Computer Science</i>. 2023;24(2). doi:<a href=\"https://doi.org/10.46298/DMTCS.8383\">10.46298/DMTCS.8383</a>","mla":"Biniaz, Ahmad, et al. “Token Swapping on Trees.” <i>Discrete Mathematics and Theoretical Computer Science</i>, vol. 24, no. 2, 9, EPI Sciences, 2023, doi:<a href=\"https://doi.org/10.46298/DMTCS.8383\">10.46298/DMTCS.8383</a>.","ieee":"A. Biniaz <i>et al.</i>, “Token swapping on trees,” <i>Discrete Mathematics and Theoretical Computer Science</i>, vol. 24, no. 2. EPI Sciences, 2023.","apa":"Biniaz, A., Jain, K., Lubiw, A., Masárová, Z., Miltzow, T., Mondal, D., … Turcotte, A. (2023). Token swapping on trees. <i>Discrete Mathematics and Theoretical Computer Science</i>. EPI Sciences. <a href=\"https://doi.org/10.46298/DMTCS.8383\">https://doi.org/10.46298/DMTCS.8383</a>","chicago":"Biniaz, Ahmad, Kshitij Jain, Anna Lubiw, Zuzana Masárová, Tillmann Miltzow, Debajyoti Mondal, Anurag Murty Naredla, Josef Tkadlec, and Alexi Turcotte. “Token Swapping on Trees.” <i>Discrete Mathematics and Theoretical Computer Science</i>. EPI Sciences, 2023. <a href=\"https://doi.org/10.46298/DMTCS.8383\">https://doi.org/10.46298/DMTCS.8383</a>.","ista":"Biniaz A, Jain K, Lubiw A, Masárová Z, Miltzow T, Mondal D, Naredla AM, Tkadlec J, Turcotte A. 2023. Token swapping on trees. Discrete Mathematics and Theoretical Computer Science. 24(2), 9."},"article_processing_charge":"No","oa":1,"author":[{"full_name":"Biniaz, Ahmad","first_name":"Ahmad","last_name":"Biniaz"},{"full_name":"Jain, Kshitij","first_name":"Kshitij","last_name":"Jain"},{"full_name":"Lubiw, Anna","first_name":"Anna","last_name":"Lubiw"},{"orcid":"0000-0002-6660-1322","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","full_name":"Masárová, Zuzana","first_name":"Zuzana","last_name":"Masárová"},{"full_name":"Miltzow, Tillmann","first_name":"Tillmann","last_name":"Miltzow"},{"last_name":"Mondal","full_name":"Mondal, Debajyoti","first_name":"Debajyoti"},{"full_name":"Naredla, Anurag Murty","first_name":"Anurag Murty","last_name":"Naredla"},{"last_name":"Tkadlec","full_name":"Tkadlec, Josef","first_name":"Josef","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1097-9684"},{"last_name":"Turcotte","first_name":"Alexi","full_name":"Turcotte, Alexi"}],"intvolume":"        24","oa_version":"Published Version","issue":"2","date_updated":"2024-01-04T12:42:09Z","publication_identifier":{"issn":["1462-7264"],"eissn":["1365-8050"]},"date_published":"2023-01-18T00:00:00Z","abstract":[{"lang":"eng","text":"The input to the token swapping problem is a graph with vertices v1, v2, . . . , vn, and n tokens with labels 1,2, . . . , n, one on each vertex. The goal is to get token i to vertex vi for all i= 1, . . . , n using a minimum number of swaps, where a swap exchanges the tokens on the endpoints of an edge.Token swapping on a tree, also known as “sorting with a transposition tree,” is not known to be in P nor NP-complete. We present some partial results: 1. An optimum swap sequence may need to perform a swap on a leaf vertex that has the correct token (a “happy leaf”), disproving a conjecture of Vaughan. 2. Any algorithm that fixes happy leaves—as all known approximation algorithms for the problem do—has approximation factor at least 4/3. Furthermore, the two best-known 2-approximation algorithms have approximation factor exactly 2. 3. A generalized problem—weighted coloured token swapping—is NP-complete on trees, but solvable in polynomial time on paths and stars. In this version, tokens and vertices have colours, and colours have weights. The goal is to get every token to a vertex of the same colour, and the cost of a swap is the sum of the weights of the two tokens involved."}],"department":[{"_id":"KrCh"},{"_id":"HeEd"},{"_id":"UlWa"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","doi":"10.46298/DMTCS.8383","status":"public","article_type":"original","volume":24,"_id":"12833","publication":"Discrete Mathematics and Theoretical Computer Science","external_id":{"arxiv":["1903.06981"]},"type":"journal_article","day":"18","scopus_import":"1"}