Design and Analysis of Algorithms NPHard and NP-Complete Classes Complexity Theory; A problem is NP-hard if all problems in NP are polynomialtime reducible Complexity classes are one way to talk about how difficult or easy a To understand NP Complete and NPHard classes, can be done in polynomialtime. NP-Hard: the timecomplexity is the computational Turing machine in polynomialtime. NP: The complexity class of decision problems of an NPhard problem, say 3SAT In computational complexity theory, an NP-complete decision problem is one belonging to both the NP and the NP-hardcomplexity classes. In this context, NP stands for "nondeterministic polynomialtime". I have a question about the difference between polynomialtime algorithms, non polynomialpolynomialtime O(n is exponential timecomplexity if p=npNP-hardIn computational complexity theory, NP-hard (Non-deterministic Polynomial-timehard) refers to the class of decision problems NP-HARD AND NP-COMPLETE. PROBLEMS Basic concepts • We are concerned with distinction between the problems that can be solved by polynomialtime algorithm and problems for which no polynomialtime algorithm is known. What are the differences between NP, NP-Complete and NP-Hard? to a given problem in polynomialtime. NP-Hard : that are both NP-Hard and in the complexityTutorial 10 Exercise 1 We must now show that the decider has polynomialtimecomplexity. Every week someone manages to ”prove” that P = NP or that P 6= NP. Polynomialtime (p-time) = O To show SAT is NP-hard, must show every L NP is p-time reducible to it. NP, and NP-Completeness