Bossek, J. and Sudholt, D. orcid.org/0000-0001-6020-1646 (2019) Time complexity analysis of RLS and (1 + 1) EA for the edge coloring problem. In: FOGA '19- Proceedings of the 15th ACM/SIGEVO Conference on Foundations of Genetic Algorithms. 15th ACM/SIGEVO Conference on Foundations of Genetic Algorithms, 27-29 Aug 2019, Potsdam, Germany. ACM Digital Library ISBN 9781450362542
Abstract
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 Δ can be colored with Δ or Δ + 1 colors, but it is NP-hard to determine whether Δ 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 (2Δ - 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(Δℓ2m log m), where m is the number of edges and ℓ is the length of the longest simple path in the graph.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2019 The Authors. This is an author-produced version of a paper subsequently published in Proceedings of the 15th ACM/SIGEVO Conference. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Edge coloring problem; runtime analysis |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 17 Oct 2019 14:21 |
Last Modified: | 18 Oct 2019 02:02 |
Published Version: | https://dl.acm.org/authorize?N680205 |
Status: | Published |
Publisher: | ACM Digital Library |
Refereed: | Yes |
Identification Number: | 10.1145/3299904.3340311 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:150551 |