What is the optimal number of threads for parallelizing algorithms?

1 Thread overhead

One factor that limits the benefits of parallelization is the overhead of creating and managing threads. Each thread consumes some memory and CPU time for its stack, context switching, synchronization, and communication. The more threads you have, the more overhead you incur. Therefore, you want to avoid creating too many threads that would compete for resources and reduce the efficiency of parallelization.

2 Workload characteristics

Another factor that influences the optimal number of threads is the nature of the workload that you want to parallelize. Some workloads are CPU-bound, meaning that they are limited by the computational power of the processor. Other workloads are I/O-bound, meaning that they are limited by the speed of input/output operations, such as reading from a disk or a network. CPU-bound workloads benefit more from parallelization than I/O-bound workloads, because they can use multiple cores to perform calculations faster. However, even for CPU-bound workloads, there is a limit to how much parallelization can help, depending on the degree of independence and communication among the tasks.

3 Hardware specifications

A third factor that affects the optimal number of threads is the hardware specifications of the system that runs the code. The most important hardware parameter is the number of physical cores or processors that are available. Each core can execute one thread at a time, so having more cores allows more parallelization. However, some systems also have features such as hyper-threading or simultaneous multithreading, which enable each core to run two or more threads concurrently by sharing resources. This can improve performance in some cases, but not in others, depending on the workload and the overhead.

4 Estimating the optimal number of threads

Given these factors, how can you estimate the optimal number of threads for your algorithm? There is no definitive answer, as it depends on the specific problem, code, and system that you are working with. However, a general rule of thumb is to start with the number of physical cores as a baseline, and then adjust it based on the workload characteristics and the thread overhead. For example, if your workload is CPU-bound and has low communication and synchronization among tasks, you can try increasing the number of threads slightly above the number of cores to see if it improves performance. If your workload is I/O-bound or has high communication and synchronization among tasks, you might want to reduce the number of threads below the number of cores to avoid contention and overhead. You can also use tools such as profilers or benchmarks to measure the performance of your code with different numbers of threads and find the optimal one for your case.

Parallelizing algorithms can be a great way to optimize your code and make use of your hardware resources. However, it also requires careful consideration of the factors that affect the optimal number of threads. By understanding these factors and experimenting with different numbers of threads, you can find the best balance between parallelization and overhead for your algorithm.