Parallel efficiency

Definition

Parallel efficiency is a measure of how effectively parallel computing resources are utilized to solve a problem, defined as the ratio of the speedup achieved by using multiple processors to the number of processors used. It reflects the performance of parallel algorithms, indicating how well they scale with the addition of more computing resources. High parallel efficiency suggests that adding more processors leads to proportionate gains in performance, which is critical in areas like numerical algorithms and performance metrics, where optimizing resource use directly impacts computational effectiveness.

5 Must Know Facts For Your Next Test

1. Parallel efficiency is expressed as a percentage; an efficiency of 100% indicates optimal utilization of all available processors.
2. Factors such as communication overhead and load imbalance can negatively affect parallel efficiency, making it less than ideal even with many processors.
3. In linear algebra applications, achieving high parallel efficiency is crucial because these computations often involve large data sets where resource use must be maximized.
4. Fast Fourier Transform (FFT) algorithms benefit from parallel efficiency since they can drastically reduce computation time when using multiple processors effectively.
5. Understanding parallel efficiency helps in optimizing algorithms and improving scalability, ensuring that performance gains are maximized as more computing resources are added.

Review Questions

• How does parallel efficiency impact the choice of algorithms in numerical computations?
  • Parallel efficiency directly influences the selection of algorithms used in numerical computations. When choosing an algorithm, it’s essential to consider how well it scales with additional processors. High parallel efficiency means that the algorithm can effectively utilize extra computational resources, leading to significant performance improvements. Thus, algorithms like those used for linear algebra or FFT are favored for their ability to maintain high efficiency as computational demands increase.
• Analyze the relationship between Amdahl's Law and parallel efficiency in the context of multi-processor systems.
  • Amdahl's Law presents a fundamental limitation on speedup in multi-processor systems and is closely tied to parallel efficiency. The law states that the maximum speedup achievable is constrained by the portion of a program that remains sequential. Consequently, if a large fraction of an algorithm cannot be parallelized, adding more processors will yield diminishing returns on performance. This relationship indicates that understanding both Amdahl's Law and parallel efficiency is crucial for optimizing computing performance.
• Evaluate the significance of maintaining high parallel efficiency when designing scalable algorithms for supercomputing applications.
  • Maintaining high parallel efficiency is vital when designing scalable algorithms for supercomputing applications because it ensures that resource investments lead to proportional increases in computational power. As supercomputers comprise thousands or millions of processors, low parallel efficiency can result in wasted resources and increased costs without delivering meaningful performance improvements. Thus, engineers and scientists must focus on optimizing both the algorithms and their implementations to achieve high efficiency, which ultimately enhances overall system effectiveness and productivity in tackling complex problems.

Related terms

Speedup: The factor by which a parallel algorithm is faster than its sequential counterpart, typically calculated as the time taken for the sequential execution divided by the time taken for parallel execution.

Amdahl's Law: A principle that provides a formula for predicting the theoretical maximum speedup for a task that can be parallelized, emphasizing that speedup is limited by the portion of the task that cannot be parallelized.

Scalability: The capability of a system to handle a growing amount of work or its potential to accommodate growth by adding resources without significantly impacting performance.