I think on the patio I would go with a good total weed killer as you say about the salt and vinegar method your away from cultivated ground so minimal if any effect to any other plants, in cultivated areas hoe or hand pulling is really the only option.
"You don't stop gardening because you get old, you get old because you stop gardening." - The Hampshire Hog
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Sureiy that just cuts the tops off thought, but leaves all the roots behind ...?
"You don't stop gardening because you get old, you get old because you stop gardening." - The Hampshire Hog