3 answers
2
Questions
Asked
1412 views
How would you go about parallelizing a recursive function that can't be written in for loops (like Ackermann function)?
I am a high school student and I am exploring a career in computer science, and while I've been able to solve many other similar problems, I haven't found an efficient solution for this. #computer-science #computer-programming #parallel-computing
Login to comment
3 answers
Steve Lewis
Assistant Vice President, Cybersecurity Team Lead & Technical Product Owner | Technical Lead | Public Speaker
83
Answers
Updated
Steve’s Answer
I found a discussion about this on a technical forum that may help you:
http://softwareengineering.stackexchange.com/questions/238729/can-recursion-be-done-in-parallel-would-that-make-sense
Updated
Anuj’s Answer
Parallelizing deep, highly non-linear recursive functions like the Ackermann function requires shifting away from loop-bound data structures and using specific concurrent architectural models.
### **1. Task-Based Parallelism (Fork-Join Model)**
Instead of mapping operations to loops, use **Task Parallelism** where each recursive call is spawned as an independent, asynchronous task. Implementations like **OpenMP tasks** (`pragma omp task`) or Java's `ForkJoinPool` allow you to fork individual recursive branches onto a background queue, letting threads execute them concurrently and `join` when evaluating the final structural substitution.
### **2. Work-Stealing Runtimes**
Because a function like Ackermann creates an asymmetric, unpredictable execution tree, a standard thread pool will suffer from immense load imbalance. You must pair task parallelism with a **work-stealing scheduler** (built into frameworks like Intel TBB or Go's goroutine runtime). When a thread finishes its deeply recursive branch early, it dynamically "steals" pending recursive tasks from the back of an overworked thread’s queue.
### **3. Concurrent Memoization (The Cache)**
The Ackermann function repeatedly recalculates the exact same state variants millions of times ($e.g.$, calculating $A(m, n-1)$ multiple times). To parallelize this effectively without thread contention, you must pair your recursive worker threads with a thread-safe, concurrent hash map or a distributed look-up table (**memoization**) so threads can immediately return pre-computed states rather than descending into duplicate deep recursive loops.
### **1. Task-Based Parallelism (Fork-Join Model)**
Instead of mapping operations to loops, use **Task Parallelism** where each recursive call is spawned as an independent, asynchronous task. Implementations like **OpenMP tasks** (`pragma omp task`) or Java's `ForkJoinPool` allow you to fork individual recursive branches onto a background queue, letting threads execute them concurrently and `join` when evaluating the final structural substitution.
### **2. Work-Stealing Runtimes**
Because a function like Ackermann creates an asymmetric, unpredictable execution tree, a standard thread pool will suffer from immense load imbalance. You must pair task parallelism with a **work-stealing scheduler** (built into frameworks like Intel TBB or Go's goroutine runtime). When a thread finishes its deeply recursive branch early, it dynamically "steals" pending recursive tasks from the back of an overworked thread’s queue.
### **3. Concurrent Memoization (The Cache)**
The Ackermann function repeatedly recalculates the exact same state variants millions of times ($e.g.$, calculating $A(m, n-1)$ multiple times). To parallelize this effectively without thread contention, you must pair your recursive worker threads with a thread-safe, concurrent hash map or a distributed look-up table (**memoization**) so threads can immediately return pre-computed states rather than descending into duplicate deep recursive loops.
Updated
Manish’s Answer
Excerpted from: https://www.daviddarling.info/encyclopedia/A/Ackermann_function.html
The Ackermann function can only be calculated using a while loop, which keeps repeating an action until an associated test returns false. Such loops are essential when the programmer doesn't know at the outset how many times the loop will be traversed. (It's now known that everything computable can be programmed using while loops
The Ackermann function can only be calculated using a while loop, which keeps repeating an action until an associated test returns false. Such loops are essential when the programmer doesn't know at the outset how many times the loop will be traversed. (It's now known that everything computable can be programmed using while loops