• Dr. Sushil Kumar Saini

NP-hard and NP-soft problems are important concepts in computer science and mathematics that describe the computational complexity of problems. NP-hard problems are believed to be inherently difficult to solve efficiently, while NP-soft problems can be solved in polynomial time. These classifications are used to determine the feasibility of finding efficient algorithms for solving problems and have led to the development of approximation algorithms and other techniques for solving real-world problems. The formal definitions of these problem classes are based on their asymptotic computational complexity and are theoretical, although they have practical implications for the difficulty of solving problems in practice. This paper investigated about the basic of NP-hard and NP-soft problems, Mathematical form and understanding of NP-hard and NP-soft problems, Significance of NP Hard and Soft Problem and existing work.

NP-hard, NP-soft, Computational Complexity, Computational Complexity

"A study and explore the significance of NP Hard and Soft Problem", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.10, Issue 3, page no.i369-i377, March-2023, Available :http://www.jetir.org/papers/JETIR2303854.pdf

"A study and explore the significance of NP Hard and Soft Problem", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.10, Issue 3, page no. ppi369-i377, March-2023, Available at : http://www.jetir.org/papers/JETIR2303854.pdf