[{"publication_identifier":{"isbn":["9783959773683"],"issn":["1868-8969"]},"arxiv":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"article_number":"4","date_published":"2025-06-02T00:00:00Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","status":"public","month":"06","publication":"4th Symposium on Algorithmic Foundations of Dynamic Networks","date_created":"2025-06-22T22:02:06Z","oa":1,"OA_place":"publisher","scopus_import":"1","ec_funded":1,"abstract":[{"lang":"eng","text":"Given a graph G that undergoes a sequence of edge insertions and deletions, we study the Maximum k-Edge Coloring problem (MkEC): Having access to k different colors, color as many edges of G as possible such that no two adjacent edges share the same color. While this problem is different from simply maintaining a b-matching with b = k, the two problems are related. However, maximum b-matching can be solved efficiently in the static setting, whereas MkEC is NP-hard and even APX-hard for k ≥ 2. \r\nWe present new results on both problems: For b-matching, we show a new integrality gap result and we adapt Wajc’s matching sparsification scheme [David Wajc, 2020] for the case where b is a constant.\r\nUsing these as basis, we give three new algorithms for the dynamic MkEC problem: Our MatchO algorithm builds on the dynamic (2+ε)-approximation algorithm of Bhattacharya, Gupta, and Mohan [Sayan Bhattacharya et al., 2017] for b-matching and achieves a (2+ε)(k+1)/k-approximation in O(poly(log n, ε^-1)) update time against an oblivious adversary. Our MatchA algorithm builds on the dynamic (7+ε)-approximation algorithm by Bhattacharya, Henzinger, and Italiano [Sayan Bhattacharya et al., 2015] for fractional b-matching and achieves a (7+ε)(3k+3)/(3k-1)-approximation in O(poly(log n, ε^-1)) update time against an adaptive adversary. Moreover, our reductions use the dynamic b-matching algorithm as a black box, so any future improvement in the approximation ratio for dynamic b-matching will automatically translate into a better approximation ratio for our algorithms. Finally, we present a greedy algorithm with O(Δ+k) update time, which guarantees a 2.16 approximation factor."}],"language":[{"iso":"eng"}],"corr_author":"1","_id":"19858","OA_type":"gold","intvolume":"       330","oa_version":"Published Version","doi":"10.4230/LIPIcs.SAND.2025.4","citation":{"ama":"El-Hayek A, Hanauer K, Henzinger M. On b-matching and fully-dynamic maximum k-edge coloring. In: <i>4th Symposium on Algorithmic Foundations of Dynamic Networks</i>. Vol 330. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2025. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SAND.2025.4\">10.4230/LIPIcs.SAND.2025.4</a>","chicago":"El-Hayek, Antoine, Kathrin Hanauer, and Monika Henzinger. “On B-Matching and Fully-Dynamic Maximum k-Edge Coloring.” In <i>4th Symposium on Algorithmic Foundations of Dynamic Networks</i>, Vol. 330. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025. <a href=\"https://doi.org/10.4230/LIPIcs.SAND.2025.4\">https://doi.org/10.4230/LIPIcs.SAND.2025.4</a>.","ieee":"A. El-Hayek, K. Hanauer, and M. Henzinger, “On b-matching and fully-dynamic maximum k-edge coloring,” in <i>4th Symposium on Algorithmic Foundations of Dynamic Networks</i>, Liverpool, United Kingdom, 2025, vol. 330.","apa":"El-Hayek, A., Hanauer, K., &#38; Henzinger, M. (2025). On b-matching and fully-dynamic maximum k-edge coloring. In <i>4th Symposium on Algorithmic Foundations of Dynamic Networks</i> (Vol. 330). Liverpool, United Kingdom: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SAND.2025.4\">https://doi.org/10.4230/LIPIcs.SAND.2025.4</a>","mla":"El-Hayek, Antoine, et al. “On B-Matching and Fully-Dynamic Maximum k-Edge Coloring.” <i>4th Symposium on Algorithmic Foundations of Dynamic Networks</i>, vol. 330, 4, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SAND.2025.4\">10.4230/LIPIcs.SAND.2025.4</a>.","ista":"El-Hayek A, Hanauer K, Henzinger M. 2025. On b-matching and fully-dynamic maximum k-edge coloring. 4th Symposium on Algorithmic Foundations of Dynamic Networks. SAND: Symposium on Algorithmic Foundations of Dynamic Networks, LIPIcs, vol. 330, 4.","short":"A. El-Hayek, K. Hanauer, M. Henzinger, in:, 4th Symposium on Algorithmic Foundations of Dynamic Networks, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025."},"isi":1,"acknowledgement":"This project has received funding from the European Research Council (ERC) under the\r\nEuropean Union’s Horizon 2020 research and innovation programme (MoDynStruct, No. 101019564) and the Austrian Science Fund (FWF) grant DOI 10.55776/Z422, grant DOI 10.55776/I5982, and grant DOI 10.55776/P33775 with additional funding from the netidee SCIENCE Stiftung, 2020–2024. This work was further supported by the Federal Ministry of Education and Research (BMBF) project, 6G-RIC: 6G Research and Innovation Cluster, grant 16KISK020K.","alternative_title":["LIPIcs"],"year":"2025","volume":330,"day":"02","conference":{"location":"Liverpool, United Kingdom","start_date":"2025-06-09","name":"SAND: Symposium on Algorithmic Foundations of Dynamic Networks","end_date":"2025-06-11"},"external_id":{"isi":["001532136900004"],"arxiv":["2310.01149"]},"project":[{"_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","name":"The design and evaluation of modern fully dynamic data structures","call_identifier":"H2020","grant_number":"101019564"},{"grant_number":"Z00422","name":"Efficient algorithms","_id":"34def286-11ca-11ed-8bc3-da5948e1613c"},{"name":"Static and Dynamic Hierarchical Graph Decompositions","_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103","grant_number":"I05982"},{"name":"Fast Algorithms for a Reactive Network Layer","_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe","grant_number":"P33775"}],"file_date_updated":"2025-06-23T11:23:29Z","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","ddc":["000"],"author":[{"orcid":"0000-0003-4268-7368","last_name":"El-Hayek","id":"888a098e-fcac-11ee-aff7-d347be57b725","first_name":"Antoine","full_name":"El-Hayek, Antoine"},{"last_name":"Hanauer","first_name":"Kathrin","full_name":"Hanauer, Kathrin"},{"id":"540c9bbd-f2de-11ec-812d-d04a5be85630","orcid":"0000-0002-5008-6530","last_name":"Henzinger","full_name":"Henzinger, Monika H","first_name":"Monika H"}],"quality_controlled":"1","article_processing_charge":"No","department":[{"_id":"MoHe"}],"title":"On b-matching and fully-dynamic maximum k-edge coloring","date_updated":"2025-09-30T13:37:28Z","has_accepted_license":"1","publication_status":"published","type":"conference","file":[{"date_updated":"2025-06-23T11:23:29Z","checksum":"ad93a1e052adb29d7bfe8bd551bab193","access_level":"open_access","file_id":"19872","date_created":"2025-06-23T11:23:29Z","success":1,"file_size":995666,"file_name":"2025_LIPIcs_ElHayek.pdf","content_type":"application/pdf","creator":"dernst","relation":"main_file"}]}]