Approaches to Comparing Cut-Set Enumeration Algorithms

It is inadequate to compare computation algorithms solely by running programs on standard examples, especially small examples. Running-time and storage-requirements should be reported for a range of problem sizes. Procedures whose resource consumption grows exponentially with problem size (e.g. cut-set enumeration) can never solve large examples, even if one fine-tunes the code for maximum efficiency. It is necessary to judge an algorithm by criteria which are independent of the particular implementation (i.e. machine, language, data representation, or programmer). Number of cut-sets generated is one such measure; the number of pairs of cut-sets checked for containment is a much better measure of computing time. Computational efficiencies of bottom-up and top-down approaches are compared. It appears that bottom-up approaches are superior if modules are elaborated separately, but the margin of superiority is not over-whelming. Finally, when a data representation is suggested, favorable and unfavorable behaviors of the representation must be analyzed. The analysis is illustrated for three representations used for cut-sets.