you need to remove the cause of this mildew or mold. Cut away over hanging branches. Open the area up for more ventilation and sun shine.
You have this because of dampness and lack of ventillation and sunlight. fix this and the problem will go away.
But now, bleach will work on the spot and the drip marks or run marks of the bleach will also clean the comp shingles all the way down. So you might have some clean run marks too.
If its a new roof, sometimes the manufacturer has accidently added some iron particles or even iron in the chat on the shingle itself. These will cause iron rust running marks too. If caught soon enough after installation, the roof can be replaced under warranty.