(untitled) (The Nepali Mathematical Sciences Report, 2025)
Computational problems and their complexity analysis play a crucial role in computer science, mathematics, and real-world applications. Such tasks can be solved using computational processes known as an algorithms. Such a process consists of a set of inputs and corresponding outputs that satisfy certain conditions. Search, decision, and optimization problems are different variants of the computational problems. Complexity theory studies the measure of efficiency in solving such problems. Such a measure is expressed in terms of space and time. Regarding time complexity, its major variants include: (i) P: polynomial time, (ii) NP: nondeterministic polynomial time, (iii) NP-complete, and (iv) NP-hard. Understanding computational complexity is essential for designing efficient algorithms, optimizing resources, and making informed decisions about problem-solving approaches. This work offers a comprehensive overview of computational problems and their associated complexities and opens a wide horizon for in-depth and broader research in this area.