Open taktoa opened 6 years ago
Average-case analysis of incremental topological ordering examines the average-case behavior of some of the incremental SCC algorithms that were superceded in the paper by Bender et al. mentioned above. Might be worth seeing if there are any papers on the average-case performance of the Bender algorithm.
Other relevant questions:
It seems like it would be quite useful (e.g.: for implementing perfect sharing) to maintain the graph of strongly-connected components of a PEG/EPEG while we build up the graph. The current state of the art online algorithm for computation of strongly-connected components is described in A New Approach to Incremental Cycle Detection and Related Problems. Technically there are two algorithms described in that paper: one that has the best known complexity bound for sparse graphs and one that has the best bound for dense graphs. It seems likely to me that PEGs are mostly going to be sparse, though I may be underestimating the amount of sharing they have. Of course, in this regime I suspect the constant factors may matter more than the difference between an
O(min(m^{3/2}, mn^{2/3}))
algorithm and anO(n^2 log(n))
algorithm.