I've tried allsorts, bleach, salt, moss killers etc and the only sure way to get rid of it is with a powerful jet wash.
The rotary path cleaners you can buy to use with the jet wash work OK to get rid of 90% and the rest with the jet wash.
Ours is a tarmac drive with a brick (pave) edging and I was concerned the tarmac might start to break up but it's been done 3 or 4 time and no sign of deterioration. Best of luck it's a fairly slow boring process.