{"issue":"2","oa_version":"None","title":"Constant-time Dynamic (Δ +1)-Coloring","quality_controlled":"1","scopus_import":"1","intvolume":"        18","language":[{"iso":"eng"}],"date_published":"2022-03-04T00:00:00Z","year":"2022","article_type":"original","publisher":"Association for Computing Machinery (ACM)","day":"04","publication":"ACM Transactions on Algorithms","publication_status":"published","article_number":"16","abstract":[{"text":"We give a fully dynamic (Las-Vegas style) algorithm with constant expected amortized time per update that maintains a proper (Δ +1)-vertex coloring of a graph with maximum degree at most Δ. This improves upon the previous O(log Δ)-time algorithm by Bhattacharya et al. (SODA 2018). Our algorithm uses an approach based on assigning random ranks to vertices and does not need to maintain a hierarchical graph decomposition. We show that our result does not only have optimal running time but is also optimal in the sense that already deciding whether a Δ-coloring exists in a dynamically changing graph with maximum degree at most Δ takes Ω (log n) time per operation.","lang":"eng"}],"doi":"10.1145/3501403","author":[{"id":"540c9bbd-f2de-11ec-812d-d04a5be85630","last_name":"Henzinger","orcid":"0000-0002-5008-6530","full_name":"Henzinger, Monika H","first_name":"Monika H"},{"last_name":"Peng","full_name":"Peng, Pan","first_name":"Pan"}],"_id":"11662","publication_identifier":{"eissn":["1549-6333"],"issn":["1549-6325"]},"volume":18,"date_updated":"2022-07-27T11:08:13Z","type":"journal_article","extern":"1","user_id":"72615eeb-f1f3-11ec-aa25-d4573ddc34fd","status":"public","citation":{"ieee":"M. H. Henzinger and P. Peng, “Constant-time Dynamic (Δ +1)-Coloring,” <i>ACM Transactions on Algorithms</i>, vol. 18, no. 2. Association for Computing Machinery (ACM), 2022.","ama":"Henzinger MH, Peng P. Constant-time Dynamic (Δ +1)-Coloring. <i>ACM Transactions on Algorithms</i>. 2022;18(2). doi:<a href=\"https://doi.org/10.1145/3501403\">10.1145/3501403</a>","mla":"Henzinger, Monika H., and Pan Peng. “Constant-Time Dynamic (Δ +1)-Coloring.” <i>ACM Transactions on Algorithms</i>, vol. 18, no. 2, 16, Association for Computing Machinery (ACM), 2022, doi:<a href=\"https://doi.org/10.1145/3501403\">10.1145/3501403</a>.","short":"M.H. Henzinger, P. Peng, ACM Transactions on Algorithms 18 (2022).","apa":"Henzinger, M. H., &#38; Peng, P. (2022). Constant-time Dynamic (Δ +1)-Coloring. <i>ACM Transactions on Algorithms</i>. Association for Computing Machinery (ACM). <a href=\"https://doi.org/10.1145/3501403\">https://doi.org/10.1145/3501403</a>","chicago":"Henzinger, Monika H, and Pan Peng. “Constant-Time Dynamic (Δ +1)-Coloring.” <i>ACM Transactions on Algorithms</i>. Association for Computing Machinery (ACM), 2022. <a href=\"https://doi.org/10.1145/3501403\">https://doi.org/10.1145/3501403</a>.","ista":"Henzinger MH, Peng P. 2022. Constant-time Dynamic (Δ +1)-Coloring. ACM Transactions on Algorithms. 18(2), 16."},"date_created":"2022-07-27T10:58:53Z","month":"03","article_processing_charge":"No","acknowledgement":"We want to thank an anonymous referee who pointed out a mistake in our conference paper as well as suggesting a fix using an approach in References."}