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Intermediate Topic 34 of 51 Concurrency & Parallelism

Parallel Prefix Sum

Scan primitive computing running totals in parallel.

How it works

The prefix sum, or scan, computes for an array the running totals: output i is the sum of inputs up to i, inclusive or exclusive. Despite its apparently sequential dependency, it can be done in parallel in O(log n) steps: the Hillis-Steele algorithm does O(n log n) work with simple structure, while the Blelloch work-efficient algorithm uses an up-sweep reduction tree followed by a down-sweep to do O(n) work. Scans work for any associative operator.

Where it is used

Stream compaction, radix sort, histogram building, polynomial evaluation, allocation of output positions in parallel, lexical analysis, sparse matrix operations and many GPU algorithms use scans as primitives.

Common pitfall

Implementations must be careful about work efficiency versus steps, memory bank conflicts on GPUs and handling arrays larger than a block, requiring hierarchical scans. Inclusive and exclusive variants are easily confused. Floating-point scans differ from serial results. Use tuned libraries such as CUB, Thrust and parallel STL rather than writing your own.

Where it fits in the course

Parallel Prefix Sum is topic 34 of 51 in Concurrency & Parallelism, rated Intermediate. It follows Parallel Reduction. The next topic is OpenMP.

Practice and explore

How to study this topic

  1. Read the explanation above and restate the definition in your own words.
  2. Open the interactive lesson and answer its mini quiz.
  3. Read the common pitfall, then write a short example that avoids it.
  4. Check your understanding in the Concurrency & Parallelism quiz, and revisit the topic if you miss a question.

Frequently asked questions

What is Parallel Prefix Sum?
Scan primitive computing running totals in parallel. It belongs to Concurrency & Parallelism and is an intermediate-level topic.
Where do people use Parallel Prefix Sum?
Stream compaction, radix sort, histogram building, polynomial evaluation, allocation of output positions in parallel, lexical analysis, sparse matrix operations and many GPU algorithms use scans as primitives.
What is the most common mistake with Parallel Prefix Sum?
Implementations must be careful about work efficiency versus steps, memory bank conflicts on GPUs and handling arrays larger than a block, requiring hierarchical scans.
What should I learn before this topic?
Start with Parallel Reduction, the topic just before it in Concurrency & Parallelism.
How can I practice it?
Answer the mini quiz in the interactive lesson, then take the Concurrency & Parallelism quiz.
Is Parallel Prefix Sum hard to learn?
It is an Intermediate topic. Be comfortable with the Beginner topics in this area first, then read the common pitfall carefully, since it is where most mistakes happen.
How long does it take to learn Parallel Prefix Sum?
Most learners can read the explanation and finish the interactive lesson in under an hour. Fluency comes from applying the idea, so plan a few short practice sessions with the quiz.
Which topics are related to Parallel Prefix Sum?
Parallel Reduction, OpenMP, Fork-Join Model are closely connected. The full list is in the related topics section of this page.
What should I study after Parallel Prefix Sum?
Continue with OpenMP, the next topic in Concurrency & Parallelism.

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