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arXiv · 1811.00710

On subexponential running times for approximating directed Steiner tree and related problems

Marek Cygan·Guy Kortsarz·Bundit Laekhanukit
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Abstract

This paper concerns proving almost tight (super-polynomial) running times, for achieving desired approximation ratios for various problems. To illustrate, the question we study, let us consider the Set-Cover problem with n elements and m sets. Now we specify our goal to approximate Set-Cover to a factor of (1-d)ln n, for a given parameter 0 = 2^{n^{c d}}, for some constant 0 = exp((1+o(1)){log^{d-c}n}), for any c>0, unless the ETH is false. Our result follows by analyzing the work of Halperin and Krauthgamer [STOC, 2003]. The same lower and upper bounds hold for CST.

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Marek Cygan, Guy Kortsarz, Bundit Laekhanukit. 2018-11-02. On subexponential running times for approximating directed Steiner tree and related problems. https://arxiv.org/abs/1811.00710

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