work stealing with Parallel Computing Toolbox

Question

I have implemented a combinatorial search algorithm (for comparison to a more efficient optimization technique) and tried to improve its runtime with parfor.

Unfortunately, the work assignments appear to be very badly unbalanced.

Each subitem i has complexity of approximately nCr(N - i, 3). As you can see, the tasks i < N/4 involve significantly more work than i > 3*N/4, yet it seems MATLAB is assigning all of i < N/4 to a single worker.

Is it true that MATLAB divides the work based on equally sized subsets of the loop range?

No, this question cites the documentation saying it does not.

Is there a convenient way to rebalance this without hardcoding the number of workers (e.g. if I require exactly 4 workers in the pool, then I could swap the two lowest bits of i with two higher bits in order to ensure each worker received some mix of easy and hard tasks)?

I don't think a full "work-stealing" implementation is necessary, perhaps just assigning 1, 2, 3, 4 to the workers, then when 4 completes first, its worker begins on item 5, and so on. The size of each item is sufficiently larger than the number of iterations that I'm not too worried about the increased communication overhead.

Answer 1

If the loop iterations are indeed distributed ahead of time (which would mean that in the end, there is a single worker that will have to complete several iterations while the other workers are idle - is this really the case?), the easiest way to ensure a mix is to randomly permute the loop iterations:

permutedIterations = randperm(nIterations);
permutedResults = cell(nIterations,1); %# or whatever else you use for storing results

%# run the parfor loop, completing iterations in permuted order
parfor iIter = 1:nIterations
    permutedResults(iIter) = f(permutedIterations(iIter));
end

%# reorder results for easier subsequent analysis
results = permutedResults(permutedIterations);