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Computer Science

Parallel Computing

Amdahl's Law and Gustafson's Law

Basic Parallel Computing Terminology

Benchmarking Parallel Code

CUDA Basics for GPU Parallel Programming

Deadlocks and Livelocks

Data Locality in Parallel Algorithms

Fault Tolerance in Parallel Systems

GPU Programming Basics

Introduction to High-Performance Computing (HPC)

Locks, Mutexes, and Semaphores

Message Passing vs Shared Memory

Parallel Computing Patterns

Parallel Algorithms for Data Structures

Parallel File Systems

Parallel Computing Algorithms

Parallel Computing in Cloud Environments

Parallel Computer Architectures

Parallel Sorting Algorithms

OpenMP Directives and Clauses

Parallel Computing with Python and multiprocessing

Parallel Programming Libraries

Types of Parallelism in Computing

Speedup and Efficiency in Parallel Systems

Shared Memory Programming with Pthreads

Task and Data Parallelism

Amdahl's Law and Gustafson's Law

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Amdahl's Law

Formula: $S = \frac{1}{(1-P)+\frac{P}{N}}$ Implications: Amdahl's Law is used to find the maximum improvement to an overall system when only part of the system is improved. It shows the diminishing returns of adding more processing units.

Gustafson's Law

Formula: $S = P + (1-P)N$ Implications: Gustafson's Law addresses the shortcomings of Amdahl's Law by taking into account that the problem size can scale with the number of processors, potentially leading to linear speedup.

Amdahl's Law Limit

Formula: $S_{max} = \frac{1}{1-P}$ Implications: Amdahl's Law implies there's a theoretical maximum speedup that can be achieved regardless of the number of processors, due primarily to the serial portion of a task.

Amdahl's Balanced Law

Formula: $S = \frac{1}{(1-P)+\frac{P}{N}+E}$ Implications: Introduces the effect of communication overhead (E) in Amdahl's Law, making it more realistic for systems where the overhead cannot be ignored.

Gustafson's Law Revisited

Formula:

S = P + (1-P) \times N - E

Implications: An extension of Gustafson's Law accounting for overhead, reflecting more accurately the real-world parallel computing situations.

Parallel Overhead

Formula: $\text{Overhead} = T_{\text{serial}} - (T_{\text{parallel}} \times N)$ Implications: Provides a measure of the additional time incurred due to parallelization, which isn't accounted for in the idealized versions of Amdahl's and Gustafson's laws.

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