How does one start a literature search for a paper?

I just had a cool idea (and proof) for an interesting way to implement a common imperative algorithm that commonly has tight constraints can have those tight constraints loosened considerably and it still behave quite well with a pretty trivial invariant.

I'm 'just' a software developer who is a big fan of mathematics. I have no idea how to go about seeing if this is novel, nor how to pursue publication.

What do!?