Arghh!!! Found a bug in my "speed up" algorithm that was causing it to skip many possible DSSs and it's back to about 15 minutes for exhaustive scans for all DSSs size 2-9. However, I went back to investigate the RN/CN candidate elimination errors and they are all due to using BOX type processing within these spaces. I remember now that these transformations "violate" the normal RC sudoku restriction that a box must contain all 9 candidates. So, I guess the answer to one of my original questions, "what operations are valid in RN/CN (forget about BN) space are valid?" is answered. Any logic that depends on box constraints must be avoided in RC/CN space. This still leaves pinnings (except for box hiddens), subsets (except for boxes), coloring (except for box conjugates)... I'm modifying all of my algorithms to skip any box type logic if the grid type is RN/CN and I'll see just how far I can go. Currently I have pinnings, box/col/row restrictions (obviously cannot be used at all in RN/CN space??), DSS subsets, x-coloring, POM fishing, niceloops, ALS chains, nishio/forcing chains modified. I think it's probably sufficient to simply test RN space since CN space seems like a reflective transformation, but I'm out of my depth here.

Back to the basics - limiting DSS to sizes 2-5 is fast and finds all normal single-sector subsets as well as a maximum of 5-sector DSSs. Transposing to RN space finds additional DSSs (hidden???) and reductions that are valid, provided that I skip box restrictions. The question that I have yet to determine is whether or not this is "as good" as the RC exhaustive 15 minute search. It's definitely faster - only takes a few millisecs to find all RC/RN DSSs sized 2-5, but it's performing different reductions. I'm starting to test the top1465 using exhaustive DSS (that's 15 * 1465 = 21975 / 60 = 366 / 24 = 15 days!) worth of processing. I already have my RC/RN tests and they only took about 1 minute total. Checking against the known DSS exemplars, it looks like RC/RN DSS can accomplish similar, albeit different, reductions.

I'll post my test results in about 2-3 weeks.