Fashion a long rope out of vines. Tie one end to something sturdy and have Ariadne float across the river with the other end. Tightrope-walk across the vine to the other side.
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Beforehand, using our advantage point look if there's a place where for river braids or divisions, this is the most shallow point. Grab a stick from one of the fallen branches and use it to measure the depth of the water and find a shallow path through the river braids. If we can easily walk across i.e. the water's not waist deep, do so, facing the current at a 45 degree angle. To assist Ariadne, grab one of the fallen branches and make Ariadne hold the other end, though if Ariadne lacks the height, take off our pants, tie off the cuffs, open the waistband and fill the pants legs with air to use as a flotation device for Ariadne. Tie her to ourselves using a vine.