existence of a permutation that satisfies order-constraints I would like to know if there is a simple algorithm for checking the existence of a permutation that satisfies a number of order-constraints.

For example, suppose we have a set (1, 2, 3, 4, 5) and a number of constraints:


1 should be before 2
2 should be before 4 
4 should be before 1


(which is of course infeasible).

Is there a simple algorithm for checking the feasibility of order-constraints? (that does not rely on lp-solvers)?

I do not have anything against Lp-solving, but i suspect that simpler algorithms are available.
Yes. ​ That task is called topological sorting.