Abstract
We investigate a natural online version of the well-known Maximum Directed Cut problem on DAGs. We propose a deterministic algorithm and show that it achieves a competitive ratio of \(\frac{3\sqrt{3}}{2}\approx 2.5981\). We then give a lower bound argument to show that no deterministic algorithm can achieve a ratio of \(\frac{3\sqrt{3}}{2}-\epsilon\) for any ε>0 thus showing that our algorithm is essentially optimal. Then, we extend our technique to improve upon the analysis of an old result: we show that greedily derandomizing the trivial randomized algorithm for MaxDiCut in general graphs improves the competitive ratio from 4 to 3, and also provide a tight example.
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Bar-Noy, A., Lampis, M. Online maximum directed cut. J Comb Optim 24, 52–64 (2012). https://doi.org/10.1007/s10878-010-9318-6
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DOI: https://doi.org/10.1007/s10878-010-9318-6