Simple wriggling is hard unless you are a fat hippo

Authors:
Irina Kostitsyna;Valentin Polishchuk
Affiliations:
Computer Science department, Stony Brook University, Stony Brook, NY;Helsinki Institute for Information Technology, Computer Science department, University of Helsinki, Finland
Venue:
FUN'10 Proceedings of the 5th international conference on Fun with algorithms
Year:
2010

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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.