Owing Graph Minimization

http://anthony-zhang.me/blog/owing-graph/index.html

by rgawdzik • 11 years ago

13 6 11 years ago

chaoxu• 11 years ago

Another way to think of this problem is find a feasible flow in a complete graph that satisfy all vertex demands and using minimum number of edges.

justinnhli2• 11 years ago

I'm confused. The article seems to require that people pay whoever they owe, as opposed to whoever is owed money. It seems we can simply sort the people by the amount owed, then have the person at the top of that list pay the person at the bottom, and repeat until all debt is resolved. This is an nlog(n) algorithm (for the sorting), and creates at most n edges (since, for every transaction, someone either pays back everything they owe, or someone gets paid everything they are owed).

Is there something I'm missing?

dragonwriter2• 11 years ago

The article seems to require that people pay whoever they owe, as opposed to whoever is owed money. It seems we can simply sort the people by the amount owed, then have the person at the top of that list pay the person at the bottom, and repeat until all debt is resolved.

You could, but that's a solution to a different problem, not a different solution to the same problem. (Which is the right problem to solve is a social/customer/domain issue, rather than a technical one.)

justinnhli2• 11 years ago

How is it different? By the definition of equivalent in the article:

when everyone in either graph pays the amounts they owe everyone else, they end up with the same amounts in the end.

It seems my algorithm also accomplishes that goal. I'm not sure that my algorithm is optimal, but I do think it's a good approximation and is somewhat simpler than the approximation in the article.

sophacles• 11 years ago

The output list makes the tuples different than the input... there is no way that john suddenly owes beryl 25 for example.

I don't see an explanation for this in the text - but a directed edge seems to switch from a semantic of "owes" to "is owed".

Owing Graph Minimization

Related Stories