What is the super-linear speedup?

The technical definition of speedup is the ratio of the time taken for the computation of a task on multiple processing units compared to a single unit. We can further explain it as the improvement in performance achieved by executing a program through parallel computing. Let's understand this concept through an example. It can be simplified by comparing the time a single mason takes to construct a brick wall to the time taken for multiple masons to construct a similar brick wall.

Assuming no other external factor, we can deduce that the latter working method proves to be an improvement. The simple ratio of this difference can be called a speedup. Similarly, in the field of parallel distributed computing (PDC), the speedup is observed when certain parts of the system are improved, typically the number of processors.

The speedup can be identified in three general models:

Fixed-size speedup: In this model, the problem size (n) is fixed, and the number of processors (p) is varied.
Scaled speedup: In this model, the problem size (n) and the number of processors (p) are varied so that the problem size per processor remains constant.
Fixed-time speedup: In this model, both the problem size (n) and the number of processors (p) are varied so that the amount of work per processor remains constant.

Applications of speedup

As previously mentioned, the speedup in our Answer’s context is used in PDC. This field focuses on how the efficiency and performance of a system can be improved by dividing the workload among multiple computing devices. This kind of computing is also known as heterogeneous computing.

In this field, the speedup is used for several reasons, including:

Performance improvement: Speedup provides a quantitative performance improvement measure by leveraging multiple processing units or resources.
Scalability analysis: Speedup helps evaluate the scalability of parallel algorithms or systems by allowing us to understand how the performance scales as the problem size or the number of resources increases.
Resource utilization: Speedup helps assess the efficiency and effectiveness of resource utilization in parallel computing. It indicates whether the additional resources effectively contribute to the overall performance or if any inefficiency or contention hampers the speedup.
Algorithmic analysis: Speedup aids in comparing different parallel algorithms or implementations for the same problem.

The most common formulas to quantify the speedup are derived from Amdahl’s and Gustafson’s laws. These laws provide simplified models and assumptions, and speedup may vary significantly due to various factors, such as communication overhead, load balancing, and system-specific characteristics. Nonetheless, these laws serve as valuable tools for estimating potential speedup and understanding the impact of parallelization on performance.

Read up on the differences between Amdahl's and Gustafson's laws.

Classification of speedup

The speedup can be divided into four possible classifications:

Sub-linear speedup
Linear speedup
Perfect linear
Super-linear speedup

Sub-linear speedup

Sub-linear speedup means that the speedup gained is less than the number of processors used, as shown in the illustration above. This occurs due to factors like memory bottlenecks, increased overhead, and other limitations that prevent optimal utilization of resources.

Linear speedup

If the speedup increases linearly as the number of processors increases, it is referred to as a linear speedup. Linear speedup indicates that the overheadThe additional computational costs incurred due to parallel distributed processing, which are not directly related to the desired computation being performed. of the algorithm remains proportional to its running time, regardless of the number of processors used.

Perfect linear

Perfect linear speedup, directly proportional to the number of processors, is an ideal case but is rarely achieved in practice due to several reasons, such as memory bottlenecks, increasing overhead, and other limitations.

Super-linear speedup

The speedup can sometimes reach far beyond the limited linear speedup, known as the super-linear speedup, which means that the speedup is more significant than the number of processors used in the system.

Let's explore more about super-linear speedup.

What is super-linear speedup?

Super-linear speedup is an important subject in the field of parallel computing, and proving its existence would drastically benefit the world of computers. Many have hypothesized and claimed that super-linear speedup is impossible. Even if it were, a single-core computation of the same algorithm would be at least p (referring to the number of processors) times slower. On the other hand, some researchers have proposed that super-linear speedup is sometimes possible because a single processor has a loop overheadThe additional computational cost incurred due to the coordination and synchronization of parallel processes..

Let's take a small quiz for a better understanding.