Time Complexity of algorithms that update the Sierpinski-like and Modified Hilbert Curves

Abstract

This paper presents the time complexity of two algorithms that update space-filling curves of adaptively refined domains. The Modified Hilbert (space-filling) Curve was proposed to traverse square-shaped adaptive-refined meshes. Whereas, the Sierpinski-like (space-filling) Curve was proposed in order to traverse triangular-shaped adaptive-refined meshes. Those curves are variations of the namesimilar well-known space-filling curves, i.e. the Hilbert Curve and the Sierpinski Curve. Moreover, they ´are adapted from those classical curves that traverse regular discretized domains. This paper describes the asymptotic tight bounds of algorithms that update the Sierpinski-like and the Modified Hilbert Curves ´ space-filling curves.