{"page":"102–115","language":[{"iso":"eng"}],"publication":"Proceedings of the 15th ACM/SIGEVO Conference on Foundations of Genetic Algorithms","status":"public","_id":"48870","user_id":"102979","year":"2019","citation":{"ama":"Bossek J, Sudholt D. Time Complexity Analysis of RLS and (1 + 1) EA for the Edge Coloring Problem. In: <i>Proceedings of the 15th ACM/SIGEVO Conference on Foundations of Genetic Algorithms</i>. FOGA ’19. Association for Computing Machinery; 2019:102–115. doi:<a href=\"https://doi.org/10.1145/3299904.3340311\">10.1145/3299904.3340311</a>","bibtex":"@inproceedings{Bossek_Sudholt_2019, place={New York, NY, USA}, series={FOGA ’19}, title={Time Complexity Analysis of RLS and (1 + 1) EA for the Edge Coloring Problem}, DOI={<a href=\"https://doi.org/10.1145/3299904.3340311\">10.1145/3299904.3340311</a>}, booktitle={Proceedings of the 15th ACM/SIGEVO Conference on Foundations of Genetic Algorithms}, publisher={Association for Computing Machinery}, author={Bossek, Jakob and Sudholt, Dirk}, year={2019}, pages={102–115}, collection={FOGA ’19} }","ieee":"J. Bossek and D. Sudholt, “Time Complexity Analysis of RLS and (1 + 1) EA for the Edge Coloring Problem,” in <i>Proceedings of the 15th ACM/SIGEVO Conference on Foundations of Genetic Algorithms</i>, 2019, pp. 102–115, doi: <a href=\"https://doi.org/10.1145/3299904.3340311\">10.1145/3299904.3340311</a>.","short":"J. Bossek, D. Sudholt, in: Proceedings of the 15th ACM/SIGEVO Conference on Foundations of Genetic Algorithms, Association for Computing Machinery, New York, NY, USA, 2019, pp. 102–115.","apa":"Bossek, J., &#38; Sudholt, D. (2019). Time Complexity Analysis of RLS and (1 + 1) EA for the Edge Coloring Problem. <i>Proceedings of the 15th ACM/SIGEVO Conference on Foundations of Genetic Algorithms</i>, 102–115. <a href=\"https://doi.org/10.1145/3299904.3340311\">https://doi.org/10.1145/3299904.3340311</a>","mla":"Bossek, Jakob, and Dirk Sudholt. “Time Complexity Analysis of RLS and (1 + 1) EA for the Edge Coloring Problem.” <i>Proceedings of the 15th ACM/SIGEVO Conference on Foundations of Genetic Algorithms</i>, Association for Computing Machinery, 2019, pp. 102–115, doi:<a href=\"https://doi.org/10.1145/3299904.3340311\">10.1145/3299904.3340311</a>.","chicago":"Bossek, Jakob, and Dirk Sudholt. “Time Complexity Analysis of RLS and (1 + 1) EA for the Edge Coloring Problem.” In <i>Proceedings of the 15th ACM/SIGEVO Conference on Foundations of Genetic Algorithms</i>, 102–115. FOGA ’19. New York, NY, USA: Association for Computing Machinery, 2019. <a href=\"https://doi.org/10.1145/3299904.3340311\">https://doi.org/10.1145/3299904.3340311</a>."},"keyword":["edge coloring problem","runtime analysis"],"type":"conference","publisher":"Association for Computing Machinery","series_title":"FOGA ’19","place":"New York, NY, USA","date_updated":"2023-12-13T10:46:12Z","title":"Time Complexity Analysis of RLS and (1 + 1) EA for the Edge Coloring Problem","extern":"1","abstract":[{"text":"The edge coloring problem asks for an assignment of colors to edges of a graph such that no two incident edges share the same color and the number of colors is minimized. It is known that all graphs with maximum degree {$\\Delta$} can be colored with {$\\Delta$} or {$\\Delta$} + 1 colors, but it is NP-hard to determine whether {$\\Delta$} colors are sufficient. We present the first runtime analysis of evolutionary algorithms (EAs) for the edge coloring problem. Simple EAs such as RLS and (1+1) EA efficiently find (2{$\\Delta$} - 1)-colorings on arbitrary graphs and optimal colorings for even and odd cycles, paths, star graphs and arbitrary trees. A partial analysis for toroids also suggests efficient runtimes in bipartite graphs with many cycles. Experiments support these findings and investigate additional graph classes such as hypercubes, complete graphs and complete bipartite graphs. Theoretical and experimental results suggest that simple EAs find optimal colorings for all these graph classes in expected time O({$\\Delta\\mathscrl$}2m log m), where m is the number of edges and {$\\mathscrl$} is the length of the longest simple path in the graph.","lang":"eng"}],"publication_status":"published","date_created":"2023-11-14T15:58:56Z","doi":"10.1145/3299904.3340311","publication_identifier":{"isbn":["978-1-4503-6254-2"]},"author":[{"full_name":"Bossek, Jakob","last_name":"Bossek","id":"102979","first_name":"Jakob","orcid":"0000-0002-4121-4668"},{"first_name":"Dirk","full_name":"Sudholt, Dirk","last_name":"Sudholt"}],"department":[{"_id":"819"}]}