Polynomial-Time Reduction Purpose.Classify problems according to relative difficulty. Design algorithms.If X sp y and y can be solved in polynomial-time, then X can also be solved in polynomial time. Establish intractability.If Xsp y and X cannot be solved in polynomial-time,then y cannot be solved in polynomial time. Establish equivalence..IfX≤y and y≤pX,we use notation X≡py. \ up to cost of reduction 77 Polynomial-Time Reduction Purpose. Classify problems according to relative difficulty. Design algorithms. If X  P Y and Y can be solved in polynomial-time, then X can also be solved in polynomial time. Establish intractability. If X  P Y and X cannot be solved in polynomial-time, then Y cannot be solved in polynomial time. Establish equivalence. If X  P Y and Y  P X, we use notation X  P Y. up to cost of reduction