Load Balancing Using Bisectors — A Tight Average-Case Analysis

Parallel Load Balancing for Problems with Good Bisectors

“…Such an assumption is valid, for example, if the problems are represented by lists of elements taken from an ordered set and if a list is bisected by choosing a random pivot element and partitioning the list into those elements that are smaller than the pivot and those that are larger. Some of the experimental results for Algorithm HF (see below) were confirmed by thorough mathematical analysis in [5]. Note that our experimental results depend on our stochastic assumptions; in applications where such assumptions are not valid, the algorithms may exhibit a different behavior.…”

“…Figures 2 6 reveal that the average ratio produced by Algorithm HF is almost constant for the whole range of N=32 to N=2 20 =1,048,567 processors and [5] shows that the ratio is indeed sharply concentrated around 2 for sufficiently large N. The good performance of Algorithm HF is due to the length of the interval from which the bisection parameter is drawn which is at least 0.15 in each simulation setup. Therefore, bisections with small :^are compensated by bisections that generate subproblems with roughly equal weight.…”

“…However, as can be seen from the simulation results presented in Section 4 as well as the average-case analysis provided by [5], the maximum load achieved by Algorithm HF is much smaller than the worst-case bound for many problem instances, especially when : is small. Therefore, the balancing quality of this approach would often be worse than what can be achieved if all available processors are used.…”

Processing a trillion cells per mouse click

“…The iteration is stopped once no chunk with more rows than a given threshold, e.g., 50'000, exists. This "heaviest first" splitting generally leads to very evenly distributed chunk sizes (for an analysis in a theoretical framework see [8]).…”