On the Maximum Span of Fixed-Angle Chains

Soss proved that it is NP-hard to find the maximum flat span of a fixed-angle polygonal chain: the largest distance achievable between the endpoints in a planar embedding. These fixed-angle chains can serve as models of protein backbones. The corresponding problem in 3D is open. We show that two special cases of particular relevance to the protein model are solvable in polynomial time: when all link lengths are equal, and all angles are equal, the maximum 3D span is achieved in a flat configuration and can be computed in constant time. When all angles are equal (but the link lengths arbitrary), the maximum 3D span is in general nonplanar but can be found in polynomial time