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I am trying to understand the euclidean TSP algorithm. From most of the explanations available online, we set the value of L = 4n^2.

is there any explanation for why L has that value?

resources

Here is the link to the source http://viswa.engin.umich.edu/wp-content/uploads/sites/169/2019/03/9.pdf

ryan chandra
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  • This is a question for the CS Stack Exchange, but to answer it quickly here, we want to snap all of the points to integers for later in the algorithm, and not have it perturb the (relative) objective too much. 4n^2 is "enough" (cf. Lemma 2.1) but you could take L larger (at the expense of running time) or smaller (to something on the order of n/epsilon, I think, at the expense of potentially having to track its contribution to the approximation ratio more carefully). – David Eisenstat Oct 17 '22 at 16:03

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