The Tool Desk
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When parallelism can speed up an algorithm
Parallelism helps when a computation contains independent tasks that can run at the same time on multiple processing units. The tasks must be large enough to keep those units busy, and the time saved by concurrent work must exceed the costs of managing it.
For example, processing separate datasets can offer a straightforward opportunity: each dataset can often be handled independently, with relatively little communication between workers. This can increase throughput—the amount of work completed across a collection of jobs—even when the goal is not to finish one particular job sooner. The National Research Council’s discussion of computing performance distinguishes this kind of throughput from reducing turnaround time for one fixed dataset.
For one fixed job, parallelism can reduce elapsed time when the work divides into substantial independent portions. That benefit depends on the algorithm and workload: tasks that depend on results from earlier tasks cannot all proceed at once.
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Why serial work limits speedup
Some parts of an algorithm must still run in sequence. Amdahl’s law describes the idealized speedup for a fixed-size problem as:
Speedup = 1 / (S + P/N)
Here, S is the serial fraction of the work, P is the parallel fraction, and N is the number of processors. The fractions sum to 1 in this model. Adding processors reduces the time attributed to the parallel fraction, but it does not eliminate the serial portion. As a result, the serial work limits the maximum speedup. This formula is a simplified upper-bound model, not a prediction or benchmark result; real programs also incur overhead. See Mississippi State University’s explanation of parallel computing theory and Cornell University’s Amdahl’s Law guide.
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As an illustration, the National Research Council says that if 80% of a program’s runtime could be made infinitely fast, the theoretical total speedup would be 5×. This is a mathematical example, not a measured performance result. The remaining 20% still takes time, however quickly the other portion runs.
Fixed job faster or more work in the same time?
The answer depends on what “faster” means. Cornell’s guide to Amdahl’s law describes the fixed-size perspective, while NVIDIA’s CUDA Toolkit Best Practices Guide, archived version 11.7, discusses fixed and growing workloads.
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| Scaling question | What stays fixed? | What parallelism may improve |
|---|---|---|
| Strong scaling | The problem size | Finishing the same job sooner as more processing units are added |
| Scaled or weak scaling | Often the time available, rather than the amount of work | Completing a larger workload or using a higher-resolution model in similar time |
For instance, adding processors to a fixed simulation asks whether the same simulation finishes sooner. Increasing the size of a fluid or structural grid asks whether a larger simulation can be completed in a similar amount of time. Those are different goals, so they can lead to different conclusions about whether parallelism is working well.
When parallelism can make an algorithm slower
All parallel programs have overhead. The University of Hamburg’s Parallel Computing Basics notes that at sufficiently high processor counts, a parallel program can run slower than on one processor. Common causes include:
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- Setup and scheduling: Dividing work, starting tasks, and assigning them to processors takes time. If tasks are tiny, this overhead may outweigh the useful computation.
- Communication and synchronization: Workers may need to exchange data or wait for one another at coordination points. Waiting reduces the time processors spend doing useful work. The National Research Council’s 2011 discussion describes synchronization as communication overhead among cooperating processors.
- Imbalance: If some tasks take much longer than others, processors assigned to short tasks may sit idle while the longest task finishes.
- Shared-resource contention: Workers may compete for memory bandwidth or another limited resource. Adding processors cannot help much if they are all waiting for that resource.
- Data movement: Moving data between a host and an accelerator can consume enough time to cancel out faster computation, especially when the data is transferred repeatedly.
Accelerator workloads have related constraints. Intel’s oneAPI GPU Optimization Guide, version 2024.1 advises providing enough parallel activity to fill the hardware and enough work per submission to amortize submission costs. Keeping data on the accelerator and reusing it can help spread transfer costs across more computation.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.How to tell whether parallelism helps your workload
Compare implementations using the same correct result and the same workload. Measure end-to-end elapsed time, not just the time spent inside the parallel computation: setup, transfers, synchronization, input/output, and result handling can all affect how long the job takes.
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- Choose the goal. Decide whether you need to finish a fixed job sooner or process more work in a given time.
- Profile the workload. Find where runtime is spent and estimate how much of it is genuinely parallelizable. A small parallel fraction limits fixed-job speedup.
- Check task size and dependencies. Make sure there is enough independent work, and that each task does enough useful computation to justify its scheduling and coordination.
- Measure the whole run. Include initialization, communication, data transfers, synchronization, I/O, and handling the output.
- Test realistic sizes and processor counts. Record the workload size and number of CPUs or accelerators. Compare several configurations: the best result for one workload may not hold for another.
This profile-then-measure approach is consistent with NVIDIA’s CUDA Best Practices Guide, which recommends identifying likely hotspots and verifying the effect of optimization.
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