Abstract
We present practical approaches for low-discrepancy 2-colorings in the hypergraph of arithmetic progressions. A simple randomized algorithm, a deterministic combinatorial algorithm (Sárközy 1974), and three estimation of distribution algorithms are compared. The best of them experimentally achieves a constant-factor approximation.
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Notes
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We have 1 TiB = 240 byte and 1 PiB = 250 byte.
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However, in [18] it is suggested to use groups with vQEA in future work.
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Even more, these 2 h is only the time spent in fitness function evaluation. Total running time was about 4 h, but we suspect this to be partly due to our implementation being not particularly suited for vQEA resulting in communication overhead.
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Acknowledgements
I thank the editors for inviting me to contribute this chapter to “A Panorama of Discrepancy Theory”. I thank Volkmar Sauerland for proofreading. I thank my co-authors from our SEA 2013 publication [11] for joint work. Financial support through DFG Priority Program “Algorithm Engineering” (Grant Sr7/12-3) is also gratefully acknowledged.
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Kliemann, L. (2014). Practical Algorithms for Low-Discrepancy 2-Colorings. In: Chen, W., Srivastav, A., Travaglini, G. (eds) A Panorama of Discrepancy Theory. Lecture Notes in Mathematics, vol 2107. Springer, Cham. https://doi.org/10.1007/978-3-319-04696-9_7
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