# Colorize buckets using the POSet and conflict graph
	fun colorize(buckets: Map[H, Set[E]]): Map[E, Int] do
		colors.clear
		for h in poset.linearize(buckets.keys) do
			var color = min_color(poset[h].direct_greaters, buckets)
			for bucket in buckets[h] do
				if colors.has_key(bucket) then continue
				while not is_color_free(color, h, buckets) do color += 1
				colors[bucket] = color
				color += 1
			end
		end
		return colors
	end