This paper uses the isoefficiency metric to analyze the scalability of several parallel algorithms for finding shortest paths between all pairs of nodes in a densely connected graph. Parallel algorithms analyzed in this paper have either been previously presented elsewhere or are small variations of them.
Scalability is analyzed with respect to mesh, hypercube and shared-memory architectures.
We demonstrate that isoefficiency functions are a compact and useful predictor of performance. In fact, previous comparative predictions of some of the algorithms based on experimental results are shown to be incorrect whereas isoefficiency functions predict correctly. We find the classic tradeoffs of hardware cost vs. time and memory vs. time to be represented here as tradeoffs of hardware cost vs. scalability and memory vs. scalability.