Not quite. Simplex is an algorithm to solve linear programming problems. Linear programming is (weakly) polynomial. The simplex algorithm itself has exponential

Not quite. Simplex is an algorithm to solve linear programming problems. Linear programming is (weakly) polynomial. The simplex algorithm itself has exponential worst case [0]. Whether there exist a polynomial-time variant of the simplex algorithm is an open problem. Constraint programming is very broad — it encompasses many types of problems. Some of them are in P, some (most?) are in NP. In principle you can use the simplex algorithm for solving certain constraint programming problems, but mostly when people talk about constraint programming they refer to different techniques. [0] https://en.wikipedia.org/wiki/Klee%E2%80%93Minty_cube https://en.wikipedia.org/wiki/Klee%E2%80%93Minty_cube