The prime competitor to algae is simply other plants. All plants consume nitrogen and phosphorus and iron. So, if there are abundant live plants in a system, what’s an algae to eat?
“Hey the plants are hogging up all the nitrogen!” (they whine bitterly)
So if there’s a handy way to put plants in the water column, DO IT. Some people simply put the plants in the pond. If you put enough in, the Koi pick on them a little, get used to them and then cohabit.
Other people net off a section of the pond and put plants in there. That’s how we set up Jimmy Carter’s pond (yes I officially care for his pond and have met him and Rosalyn) at the Carter Center in Atlanta and we just netted an area and loaded it with Hyacinths and Lettuce in the Summer and then Anachris in the Fall. (Year round nitrogen reduction)
Some people make an entirely separate vat of plants and move some water through at all times. This is much the same as bogging plants, as well.
Finally, I made some floating crates pictured above. The crate material are polyethylene floor grates for slaughter houses and such; cable tied together in the form of boxes they float and the plants are in there. Click the image above for the larger verson for study.