A (Slightly) Improved Approximation Algorithm for Metric TSP · HackerPapers discussions

A (Slightly) Improved Approximation Algorithm for Metric TSP — mentioned by mousebaiker

Fri, 09 Oct 2020 11:28:57 GMT

The original paper mentioned in the article [1] deals with metric TSP, so a triangle inequality must be satisfied. This means that you can actually find a space where the points will be the coordinates. Anyway, the grandparent solves the Euclidean TSP which is still an NP-complete problem. I will be reluctant to say that it is an easier problem in a general sense. I agree though that there are better and easier approximations for it. [1] https://arxiv.org/abs/2007.01409

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A (Slightly) Improved Approximation Algorithm for Metric TSP — mentioned by fmeyer

Thu, 08 Oct 2020 19:36:17 GMT

“The algorithm we study is very similar, except we choose a random spanning tree based on the standard linear programming relaxation of TSP.” That’s so subtle to suggest but incredible hard to prove https://arxiv.org/abs/2007.01409

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A (Slightly) Improved Approximation Algorithm for Metric TSP — mentioned by mjn

Thu, 08 Oct 2020 17:31:55 GMT

The paper is really nicely written: https://arxiv.org/abs/2007.01409 It's lengthy and full of some quite technical sections, but those are interspersed with sections sketching the high-level intuition and proving more informal versions of the technical theorems in simplified cases. An example is on p. 19, section 3.1, "Ideas underlying proof of Theorem 3.1".

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A (Slightly) Improved Approximation Algorithm for Metric TSP — mentioned by Tyr42

Thu, 08 Oct 2020 17:31:11 GMT

Oh man, it's actually a real improvement! I was afraid it was more pop sci, but not this is pretty cool. I think this is the paper? https://arxiv.org/abs/2007.01409

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