Does a mathematical modelling on Christofides algorithm exist, is it even possible to create one?

  • $\begingroup$ What is the "distribution problem" you are trying to solve? $\endgroup$ – Curtis F Dec 8 '18 at 19:45
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    $\begingroup$ Your question makes little sense I'm afraid. TSP is a problem with a precise input and output. You can say things like "I have a problem in which I need to distribute items to locations, and this problem can be modeled as an instance of TSP". But what is your question exactly? $\endgroup$ – Juho Dec 8 '18 at 19:49
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    $\begingroup$ What do you mean by "a mathematical modelling on Christofides algorithm"? The algorithm has been analyzed mathematically: that's how we know that it works and know how long it takes. $\endgroup$ – David Richerby Dec 8 '18 at 22:08
  • $\begingroup$ @SebastianNielsen Um. Christofides's original paper? Are you proposing that he just said, "Hey, here's this algorithm. I dunno if it works or anything, but you guys might find it interesting"? Wikipedia? $\endgroup$ – David Richerby Dec 8 '18 at 22:17
  • $\begingroup$ @SebastianNielsen What do you mean by "a mathematical modelling"? $\endgroup$ – David Richerby Dec 8 '18 at 22:24

The mathematical model relevant for understanding Christofides' algorithm is not the algorithm itself but rather the problem it is trying to solving – the traveling salesman problem. This is a model for optimization problems which occur in practice.

Christofides' algorithm itself could also perhaps be considered a model, if it is supposed to represent the way that humans (or animals, or nature) solve the traveling salesman problem. But in fact, it doesn't – it was designed as an efficient algorithm for computers.

  • $\begingroup$ No. What I’m saying is more like that 7 isn’t a color. $\endgroup$ – Yuval Filmus Dec 9 '18 at 9:01
  • $\begingroup$ I think that’s the root of the problem. You seem to be trying to answer a questionable quiz question. Christofides’ algorithm is an algorithm or heuristic, not a model. It’s a category error to ask if it’s a mathematical model (though not completely out of the question, as I tried to explain in my answer). I don’t think your knowledge of mathematical modeling will be furthered by trying to answer nonsensical questions like this. $\endgroup$ – Yuval Filmus Dec 9 '18 at 9:12
  • $\begingroup$ How about asking your TA or professor? $\endgroup$ – Yuval Filmus Dec 9 '18 at 9:18
  • $\begingroup$ Complain to the dean. Unfortunately we cannot fix your university on this online platform. $\endgroup$ – Yuval Filmus Dec 9 '18 at 9:24
  • $\begingroup$ In that case, your parents should contact the principal. We can’t fix the high school system online. $\endgroup$ – Yuval Filmus Dec 9 '18 at 9:32

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