Wikipedia:Reference desk/Archives/Mathematics/2018 October 30

= October 30 =

RSA type challenges other than factoring
The RSA numbers proved useful to determine what size number can be feasibly factored and to spur research into the problem. I was wondering if there were sets of challenges related to other computationally difficult problems. For example is there a set of increasingly large instances of the Traveling Salesman Problem somewhere whose answers are known, but only the problem data and not the solution are available to the public? I guess to have the same spirit as RSA the instances should have the following properties: --RDBury (talk) 17:19, 30 October 2018 (UTC)
 * A range of sizes starting with estimated computation time a few days on a PC.
 * Each instance should provably reduce to a finite, if very lengthy, computation.
 * Each instance is to a large extent randomly generated for the given size.
 * It should be easy to check if a proposed solution is correct.
 * Cash prizes a plus.
 * An anonymous user pointed out, an annual competition of SAT solvers. It's interesting to me that, while all the RSA numbers fit comfortably on a single Wikipedia page, the test files for the contest are in the megabyte range. This seems somewhat ironic since integer factorization is thought not to be NP-complete and therefore 'easier' in some sense than SAT. It looks like one reason for RSA type challenges for NP-complete problems being hard to find is that problem data files must be very large to even give modern heuristic-based algorithms a good workout. --RDBury (talk) 04:44, 2 November 2018 (UTC)