I think it's worth reviewing that cyano and problem algae actually need. kmk2307 is right that the "big three" nutrients are phosphates, nitrates, and silicates. However, our different pest species vary in which they use.
All plants, including all algae, need nitrogen and phosphorous. If you have an adequate supply of usable nitrogen and phosphorous, plus enough light to support photosynthesis, you will be growing algae. The only question is what kind.
Diatoms are a special case because they require silicon to build their shells. Lacking available silicon (silicates), diatoms can't grow. If there's plenty of silicon, however, diatoms may have an advantage. Note that diatoms need nitrogen and phosphorous just like all other plants, so it's only partiallly true that silicates "cause" diatom blooms.
At least some flavors of cyanobacteria, which isn't really a plant at all, are capable of fixing nitrogen from the air. If nitrates are in short supply, cyanobacteria has an advantage over algae.
As previously discussed, keeping your phosphates low will slow down the growth of all plant species and cyanobacteria. As many have discovered, that's harder than it sounds. Note that many phosphate test kits don't detect organic forms of phosphorous, so a reading of zero does not demonstrate a total lack.
As previously noted, skimming helps cut down on phosphates, particularly if you feed kalkwasser into the skimmer. Phosphate sponges help, but probably only work on the inorganic forms. Activated carbon will remove many of the organic forms. Note that carbon becomes saturated after a short time, so to be effective it needs to be renewed frequently.
As an adjunct strategy to combatting cyano, you might consider encouraging the growth of other plant species. Regular exports of plant material from a refugium, for instance, should help.
You might also consider dosing silicates. Given a choice, I would much rather be dealing with diatoms than cyano or hair algae. Randy Holmes-Farley doses silicates in his tank, although perhaps not for this reason. Search for silicates in the chemistry forum for information on that.