Here are the preliminaries required for designing a parallel algorithm in short steps:
1. Algorithms and Data Structures: A solid understanding of algorithms and data structures is essential to design efficient parallel algorithms. The knowledge of algorithmic techniques like divide-and-conquer, dynamic programming, and graph algorithms, and data structures like arrays, trees, graphs, and hash tables are necessary.
2. Computer Architecture: Understanding the underlying hardware architecture is crucial to designing efficient parallel algorithms. The knowledge of processors, memory, cache hierarchy, interconnect networks, and other hardware features is required.
3. Parallel Computing: Familiarity with parallel computing models, such as shared memory, distributed memory, and hybrid models, is required to design parallel algorithms. Understanding parallel programming concepts like parallelization, synchronization, and communication primitives, is essential.
4. Computational Complexity: Knowledge of computational complexity theory, including time and space complexity, is crucial to design scalable parallel algorithms. A good understanding of the classes of problems such as P, NP, and NP-hard, is necessary to determine the feasibility of parallelizing an algorithm.
5. Probability and Statistics: A strong foundation in probability and statistics is necessary to design algorithms that can handle uncertain and noisy data. Techniques like Monte Carlo methods and randomized algorithms require a good understanding of probability theory.
6. Numerical Analysis: Knowledge of numerical methods, including numerical linear algebra, optimization, and differential equations, is necessary to design parallel algorithms for scientific computing and simulation.
7. Software Engineering: Knowledge of software engineering principles, such as modular design, testing, debugging, and version control, is necessary to design reliable and maintainable parallel algorithms.
Overall, designing a parallel algorithm requires a multidisciplinary approach that combines knowledge from various fields of computer science and mathematics.