Planar configurations of fixed-angle chains and trees are well studied in polymer science and molecular biology. We prove that it is strongly NP-hard to decide whether a polygonal chain with fixed edge lengths and angles has a planar configuration without crossings. In particular, flattening is NP-hard when all the edge lengths are equal, whereas a previous (weak) NP-hardness proof used lengths that differ in size by an exponential factor. Our NP-hardness result also holds for (nonequilateral) chains with angles in the range [60° - ε,180°], whereas flattening is known to be always possible (and hence polynomially solvable) for equilateral chains with angles in the range (60°,150°) and for general chains with angles in the range [90°,180°]. We also show that the flattening problem is strongly NP-hard for equilateral fixed-angle trees, even when every angle is either 90° or 180°. Finally, we show that strong NP-hardness carries over to the previously studied problems of computing the minimum or maximum span (distance between endpoints) among non-crossing planar configurations. © 2011 Springer-Verlag.
CITATION STYLE
Demaine, E. D., & Eisenstat, S. (2011). Flattening fixed-angle chains is strongly NP-hard. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6844 LNCS, pp. 314–325). https://doi.org/10.1007/978-3-642-22300-6_27
Mendeley helps you to discover research relevant for your work.