Benchmarking optimised algorithms for transitive closure

We investigate the impact of using different algorithmic techniques and data representations in algorithms to calculate the transitive closure of a finite binary relation. These techniques are change monitor, loop fusion, loop tiling and short-circuiting. We explain them and how they are applied in the algorithms. We measured the impact of these techniques on the elapsed time to execute the algorithms, using C++ implementations with two different data representations, and using various data sets. The investigation also covers more basic transitive closure algorithms, and as a result forms a large-scale empirical comparison of such algorithms.