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24 June 2024
 
  » arxiv » 2302.00213

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Approximating Red-Blue Set Cover
Eden Chlamtáč ; Yury Makarychev ; Ali Vakilian ;
Date 1 Feb 2023
AbstractWe provide a new approximation algorithm for the Red-Blue Set Cover problem and give a new hardness result. Our approximation algorithm achieves $ ilde O(m^{1/3})$-approximation improving on the $ ilde O(m^{1/2})$-approximation due to Elkin and Peleg (where $m$ is the number of sets). Additionally, we provide a nearly approximation preserving reduction from Min $k$-Union to Red-Blue Set Cover that gives an $ ildeOmega(m^{1/4 - varepsilon})$ hardness under the Dense-vs-Random conjecture.
Source arXiv, 2302.00213
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