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. (2010). Simple Wriggling Is Hard Unless You Are a Fat Hippo. In: Boldi, P., Gargano, L. (eds) Fun with Algorithms. FUN 2010. Lecture Notes in Computer Science, vol 6099. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13122-6_27
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DOI: https://doi.org/10.1007/978-3-642-13122-6_27
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