> For the complete documentation index, see [llms.txt](https://wiki.hanzheteng.com/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://wiki.hanzheteng.com/algorithm/cs/computational-model.md).

# Computational Model

![](/files/-McaektC1vRICzPinXPk)

### Random-Access Machine (RAM)

* Unit cost for 
  * any instruction on O(log(n))-bit words
  * Read/write a single memory location from an infinite memory
* The cost measure: time complexity

variant: Parallel RAM (PRAM) model

### Fork-Join Model

* is the main model of parallel execution in the OpenMP framework
* In addition to RAM instructions, you can also use `in parallel` and `parallel for` instructions.

```cpp
mergesort(A, lo, hi):
  if lo < hi:
    mid = ⌊lo + (hi - lo) / 2⌋
    fork mergesort(A, lo, mid) // process (potentially) in parallel with main task
      mergesort(A, mid, hi)    // main task handles second recursion
    join
      merge(A, lo, mid, hi)
```

### Work-Span Model

* For all computations, draw a DAG
  * A->B means that B can be performed only when A has been finished
* **Work**: the total number of operations
* **Span** (depth): the longest length of chain

![](/files/-Mcal8btyD57on7epp8q)


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