User Tools

Site Tools


supercomputer

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
Next revision
Previous revision
supercomputer [2023/02/27 17:21]
harshec
supercomputer [2023/02/27 17:36] (current)
harshec
Line 1: Line 1:
-====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<sup>98</sup> in size with no symmetry restrictions), a factor of 1000x or so might help discover an inhomogeneous set between 18-18-18-24-30 and 20-36-36-36-36 (or, definitively rule out the existence of such sets).+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<sup>98</sup> in size with no symmetry restrictions), a factor of 1000x or so might help discover an inhomogeneous set between 18-18-18-24-30 and 20-36-36-36-36 (or, definitively rule out the existence of such sets).
  
 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.
Line 23: Line 23:
 ---- ----
  
-But, at least that "0" can be added way down the chart of [[inhomogeneous_solutions|Inhomogeneous Solution Counts]]. And, there is no doubt that more results (whether negative or positive) can be added, results that a single-core search would take months or years to accomplish.+But, at least that "0" can be added way down the chart of [[inhomogeneous_solutions|Inhomogeneous Solution Counts]]. And, there is no doubt that more results (whether negative or positive) can be added, results that a single-core search would take months or years to accomplish (next on the list: 18-18-18-30-36-m).
  
 It is at this point Eric should formally that the Alabama Supercomputer Authority by including their recommended blurb: "This work was made possible in part by a grant of high performance computing resources and technical support from the Alabama Supercomputer Authority." Any results garnered from ASA resources will include the initial "ASA" next to them. It is at this point Eric should formally that the Alabama Supercomputer Authority by including their recommended blurb: "This work was made possible in part by a grant of high performance computing resources and technical support from the Alabama Supercomputer Authority." Any results garnered from ASA resources will include the initial "ASA" next to them.
  
supercomputer.1677518497.txt.gz ยท Last modified: 2023/02/27 17:21 by harshec