# Article revision ideas

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Below, you can find a list of revision ideas for articles. If you choose to write about one of these ideas, remove it from the list below and email me.

Please do not revise your own article unless you check with me first.

Want to revise an article that's not listed here? Email me!

## List of Articles

• This article should be merged with article on the Kantorovich Dual Problem for c= d^2 -- this should be a separate section in the article.
• Add a section on the dual problem for c=d and why this is a much simpler problem.
• The precise statement of the theorem should come first, and the heuristic interpretation in terms of the Shipper's problem should come second.
• There are some grammar problems that should be fixed.
• The section on ideas of the proof should refer to the wiki articles on Fenchel-Rockafellar Duality.
• This article should be rewritten in a way that is understandable to an undergraduate who has taken vector Calculus and linear algebra. It's fine to also mention more advanced topics, to connect it to other articles on the wiki, but the point of this article is that, in the discrete setting, it is just a vector calculus problem.
• Add a sentence to the beginning of the article about the intuitive idea of discrete measures, e.g. something like ``probability vectors, where the indices of the vector correspond to the amount of mass given to different locations in space
• The formatting for the statute of the problems could be improved with more displayed equations. The organization could be improved.
• Fewer parenthetical statements would be better.
• Better formatting could help make it more clear the notion of transport plan and map in this setting. It would be good to visually distinguish the Kantorovich and Monge Problem.
• What is the analogue of the dual Kantorovich problem in the discrete setting?
• When is the Monge problem solvable in the discrete setting? (We certainly won't have absolute continuity wrt Lebesgue, but it is still solvable in many cases...)
• The sentence in the section on Useful Combinatorial Structure could be a footnotes to a pervious section.
• The Algorithms section could be changed to just be the last sentence in the introduction.