Polynomial Time Reductions
Let R and Q be two problems. We say that R is polynomially reducible to Q if there is a polynomial time algorithm that converts each input r to R to another input q to Q such that r is a yes-instance of R if and only if q is a yes-instance of Q.
Theorem: If R is polynomially reducible to Q and there is a polynomial time algorithm for Q, then there is a polynomial time algorithm for R.
Other Factoid: Polynomial reducibility is transitive.