20210923, 18:19  #67 
Aug 2020
79*6581e4;3*2539e3
616_{8} Posts 
I did the matrix building to see how many uniques were required, but yes, it's faster to just do that once and otherwise only use remdups. So I'll do just that? Or is there some merit in using msieve instead of remdups?
Would it be helpful to sieve at q > 108M? A range of 1M takes slightly more than 3 hours, so a few M can quickly be added overnight. 
20210923, 18:24  #68 
"Curtis"
Feb 2005
Riverside, CA
11577_{8} Posts 
I don't think we can answer that until we see the data from 15 vs 12 vs 10. I'm expecting 5060% duplicates in 1215, and worse in 1012.
If you do wish to take more data, I think Q=810M would tell us more about the optimal starting Q than 108+. Let's see what we learn with the data you have, first. 
20211007, 16:52  #69 
Aug 2020
79*6581e4;3*2539e3
2×199 Posts 
Total  Uniques  Duplicates  Ratio
10100M 214,512,998  153,030,781  61,482,217  71,34% 11105M 219,448,738  158,516,513  60,932,225  72,23% 12110M 224,369,197  163,859,554  60,509,643  73,03% 13110M 220,590,893  162,609,603  57,981,290  73,72% I also did several steps in between, but ran into a problem. Is it possible that the dimension parameter for remdups4 strongly influences the number of uniques found? Initially I did the remdup manually with dim close to the required maximum value. For the batch file I just used 650 because it worked for all ranges. But I found that with dim=350 I got 85,319,847 uniques for 1050M while with dim=650 it was only 83,992,074. Was that just coincidence and something else went wrong (total numbers of rels was the same though) or does the dimension influence it? I can't really imagine it, but who knows. What I was planning to do is finding the number of uniques for various ranges in 5M or 1M steps. That way it's be possible to find the ideal qmin that will reach the required 152M unqiues within the shortest range. And we'd see if that happens when qmax/qmin = 8. I don't know if sieving smaller q's makes sense, already at 10M it's much less efficient than at the larger qmins. Or do you want to see something specific from it? Last fiddled with by bur on 20211007 at 17:01 
20211007, 17:38  #70 
"Curtis"
Feb 2005
Riverside, CA
7×23×31 Posts 
I believe a toosmall dimension setting will let some duplicate relations sneak through; a reasonable price to pay to control memory use on really big problems. For these normalsized jobs, I set dim to 3000 so that it is not a factor.
As for Qmin selection, it's a more complicated problem than you think it is. Sec/rel at small Q is typically 5060% of the time at the ending Q. So, we can tolerate a quitelarge duplicate ratio at small Q because the relations are found so quickly. Q=10M might be 75% faster than Q=110M, but yield 45% duplicates vs 15% at high Q. I made up those numbers, but they're typical in the data I gathered. If that's the data, is Q=1011M worth sieving? So, if you want to more accurately solve for the best minQ on this job, you'd need: relations per second at Q=10M duplicate rate for 1011M, found by filtering 10110M and 11110M to determine how many uniques are added by sieving 1011M and then dividing by the total raw relations count for 1011M. relations per second at 110M duplicate rate for 109110M or 110111M. Even then, you'll have data for just one job, and this data varies from job to job. I suggest that Qmax/Qmin = 8 is "good enough" for our purposes. Edit: Let's look at your last two lines of data, since they have the same ending Q: 1213M has 3778304 total relations, 1249951 unique. That's a duplicate ratio of 67%, higher than I expected. If you have data for duplicate ratio above 105M, we could then convert the sieve speeds of each range into a "uniques sec/rel" speed and presto! An answer for 1213 vs 108110. Last fiddled with by VBCurtis on 20211007 at 17:45 
20211007, 17:56  #71 
Apr 2020
2^{2}·3·41 Posts 
The way I tested this was to look at the CPUtime stats in the logfile ('stats_total_cpu_time') to find ranges that took almost exactly the same length of time to sieve, and then see which of these ranges produced the most unique relations.

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