supercomputer
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supercomputer [2023/02/27 17:17] harshec |
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| - | ====A Supercomputer Joins The search==== | + | ====A Supercomputer Joins The Search==== |
| In February of 2023 Eric Harshbarger started using resources at the Alabama Supercomputer Authority to search certain spaces for possible permutation-fair sets. The hope is that such improved speeds will help fill in entries farther down the list on the page of [[inhomogeneous_solutions|Inhomogeneous Solution Counts]]. Previous reliance on single computers to conduct such searchs allowed Eric, Landon Kryger, and Brandon Enright to make quite a bit of progress in eliminating configurations by exhaustive search. However, eventually the search spaces became too large; things started becoming too big around 18-18-18-24-30 or so. | In February of 2023 Eric Harshbarger started using resources at the Alabama Supercomputer Authority to search certain spaces for possible permutation-fair sets. The hope is that such improved speeds will help fill in entries farther down the list on the page of [[inhomogeneous_solutions|Inhomogeneous Solution Counts]]. Previous reliance on single computers to conduct such searchs allowed Eric, Landon Kryger, and Brandon Enright to make quite a bit of progress in eliminating configurations by exhaustive search. However, eventually the search spaces became too large; things started becoming too big around 18-18-18-24-30 or so. | ||
| - | With the discovery of a valid 20-36-36-36-36 set by Bram Cohen in December 2022, Eric was encouraged that the use of a high performance cluster (HPC, aka, supercomputer) might help search this remaining window of configurations. An HPC will likely only speed things up by a few orders of magnitude, and while that would not help in spaces as vast as the 5d30 space (10< | + | With the discovery of a valid [[significant_solutions|20-36-36-36-36 set by Bram Cohen]] in December 2022, Eric was encouraged that the use of a high performance cluster (HPC, aka, supercomputer) might help search this remaining window of configurations. An HPC will likely only speed things up by a few orders of magnitude, and while that would not help in spaces as vast as the 5d30 space (10< |
| To take advantage of the HPC, Eric had to modify the search code in use. The original code had been written by Landon Kryger and was extraordinarily fast; but, again, it had pretty much reached its limit when running a single search on a single core processor. The java code was modified by Eric to do a couple of things. | To take advantage of the HPC, Eric had to modify the search code in use. The original code had been written by Landon Kryger and was extraordinarily fast; but, again, it had pretty much reached its limit when running a single search on a single core processor. The java code was modified by Eric to do a couple of things. | ||
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| The first successful implementation of all of this was used to search the 18-18-18-24-30-m space (that is asking: "Is there a 5-player, permutation-fair set that uses 3d18+d24+d30 and has mirror symmetry?" | The first successful implementation of all of this was used to search the 18-18-18-24-30-m space (that is asking: "Is there a 5-player, permutation-fair set that uses 3d18+d24+d30 and has mirror symmetry?" | ||
| - | First Eric generated all valid 3-player, 18-18-18-m configurations. There are 767975 of these, and it took a couple of seconds to generate them all on a laptop. Then, using the HPC, he ran eight searches in parallel (looking to see how many ways a d24 could be added to create 18-18-18-24-m solutions), partitioning those 767975 seeds into eight groups of 100000 each (the last group not having a full count). Those eight searches were completed in less than ten minutes; and each wrote out its own output file. Those output files were concatenated together into one large file, and the total number of 18-18-18-24-m configurations was confirmed to be 3159772 (this was known from a previous search done long ago). That data file of 3159772 4-player configurations was then partitioned up into 32 sections (a 100,000 configurations in each, save the final), and the HPC let loose with 32 individual, parallel searches trying to add in a d30 as a fifth die. | + | First Eric generated all valid 3-player, 18-18-18-m configurations. There are 767975 of these, and it took a couple of seconds to generate them all on a laptop. Then, using the HPC, he ran eight searches in parallel (looking to see how many ways a d24 could be added to create 18-18-18-24-m solutions), partitioning those 767975 seeds into eight groups of 100000 each (the last group not having a full count). Those eight searches were completed in less than ten minutes; and each wrote out its own output file. Those output files were concatenated together into one large file, and the total number of 18-18-18-24-m configurations was confirmed to be 3159772 (this was known from a previous search done long ago). That data file of 3159772 4-player configurations was then partitioned up into 32 sections (with 100,000 configurations in each, save the final), and the HPC let loose with 32 individual, parallel searches trying to add in a d30 as a fifth die. |
| - | An interesting thing about those parallel searches: the amount of time to complete a particular partition can vary drastically depending upon how " | + | An interesting thing about those parallel searches: the amount of time to complete a particular partition can vary drastically depending upon how " |
| The end result of all of this is rather anticlimactic: | The end result of all of this is rather anticlimactic: | ||
| ---- | ---- | ||
| - | But, at least that " | + | But, at least that " |
| - | It is at this point Eric should formally that the Alabama Supercomputer Authority by including their reccomended | + | It is at this point Eric should formally that the Alabama Supercomputer Authority by including their recommended |
supercomputer.1677518259.txt.gz ยท Last modified: 2023/02/27 17:17 by harshec
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