Abstract
We prove that it is NP-hard to decide whether two points in a polygonal domain with holes can be connected by a wire. This implies that finding any approximation to the shortest path for a long snake amidst polygonal obstacles is NP-hard. On the positive side, we show that snake’s problem is “length-tractable”: if the snake is “fat”, i.e., its length/width ratio is small, the shortest path can be computed in polynomial time.
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Kostitsyna, I., Polishchuk, V. Simple Wriggling is Hard Unless You Are a Fat Hippo. Theory Comput Syst 50, 93–110 (2012). https://doi.org/10.1007/s00224-011-9337-4
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DOI: https://doi.org/10.1007/s00224-011-9337-4