Of course, but you can't just mix and match these medications. Some have serious side effects and can't be used repeatedly, and some have interactions with other meds.
You should just ask your vet. Vets will take into account the insects in your area, as well as your dog's coat and lifestyle.
It'd be a really bad idea to just load your dogs up on meds. The risk of these parasites varies greatly by geographical region. For example, in the pacific northwest, there's no need to protect against heartworms.
I Agree. All this things are changing. New vectors and new emergent diseases are not uncommon. An example is the new feline morbilivirus, very dangerous for cats and discovered in 2012. A local and experienced vet is in the best position to have trusty local info about diseases and parasites. Webs like this can not have this info, at least in its current state. Not a bad start, but can be improved a lot.
Is the med X legal in your country?, dunno, but you can order here your dog drugs. Can I mix X and Y?, dunno, order both and read the contraindications later. Are this meds dangerous for my other pets like my "always-chewing-dog-ears" cat, or my ferret? this web don't give you any clue. I know cases of kitten killed by the wrong treatment; Can you calculate the right doses for your big but starved and weak new rescued pet?... etc, etc...
Of course the owner can and should take some time to educate itself about recognising diseases (and much specially poisonings) of his pet, but good and comprehensive manuals are available in your book store, and of course to identify what kind of roundworm could or not have your dog is not trivial at all for a normal owner.
The guy that that puts all in his tank to cure "don't know what's this thing growing in my fishes" is sadly very common in aquariums. He/she kills currently much more aquarium fishes than the real diseases do.
Are you sure about this? My wife and I fostered a dog last year (here in Southern Oregon) that had heartworms. The treatment was nasty and dangerous to the dog, but the dog did recover.
Dogs won't contract heartworms naturally here but dogs brought in from other areas are definitely at risk of already having heartworms and possibly sharing those via feces. Basically an invasive species.
>>Is there an algorithm that would find the minimum subset of these to cover every parasite/bug?
This is the same problem we have in embedded systems diagnostics. We used to make a list of failure modes, and then a list of diagnostic tests. A given test may detect multiple different failures and I've made grids exactly like this. I always advocate for finding the minimum set of tests to detect all failures (to minimize false positives and simplify software). I was going to make the same point in this case, but parent already did.
To be clear, sometimes it's sufficient to detect failure without knowing exactly what the problem was. For specific diagnostics you may want POST to handle that, but at runtime you may only need to detect that something has failed.
You should just ask your vet. Vets will take into account the insects in your area, as well as your dog's coat and lifestyle.