This question asks a question that is about an algorithm which is not a traditional part of computational science - maybe rather of theoretical computer science. If we decide these questions belong on cstheory.stackexchange.com, and such questions come up more often, then it might be good if we'd get a "move to cstheory.stackexchange.com" option in the flagging system.
Dynamic programming has come up in a linear programming class I took, and should also come up in algorithms-based computer science classes. You could, and people do, solve problems like knapsack problems using dynamic programming. Since optimization is part of scientific programming, I think it is allowable to discuss when one might use a dynamic programming approach to solve a problem.
"Implementation" is tricky, though. I think pseudocode or an algorithm sketch would be acceptable. The same poster asked for an algorithm that could be related to scientific computing in the question "How to fill a 2D set over a Cartesian lattice with as few rectangles as possible?", and no one mentioned anything about it being off-topic. The answer the poster was looking for was on Math Overflow, and a CS Theory page was linked to it also.
The question also relates to graph theory, and graph theory, particularly as it relates to answering questions about networks, is increasingly becoming a scientific computing discipline.
I am inclined to let it go, but I am really interested in hearing other people in the community weigh in so that a consensus decision can be reached.
There are two issues.
The first one is that as has been discussed on area51 before, this site was not going to overlap significantly with existing sites like cstheory. So if you are going to include what a main part of the scope of cstheory we would object to that.
The second issue is: is this really a question for cstheory or not. Being "purely algorithmic" question doesn't make it necessarily on-topic for cstheory which is for research-level *theoretical* computer science questions. But it might make it part of the new CS proposal, and I think they would object to the scope of computational sciences being extended to cover what was not part of the proposal and is part of their proposal.
I don't see why not... algorithms are an essential component of scientific computing... from theory to implementation... Although, if a question is left unanswered for too long, it might be a good idea to migrate it to the theoretical computer science stackexchange site.
thanks for raising this!
I would not be averse to keeping this question around because optimization is a related field, but I'm not sure we have anybody interested in answering it, so I guess this would be a neutral vote.
I'm interested in hearing what the rest of the community has to say though.