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

This paper presents the time complexity of two algorithms that update space-filling curvesof adaptively refined domains. The Modified Hilbert (space-filling) Curve was proposed to traversesquare-shaped adaptive-refined meshes. Whereas, the Sierpi´nski-like (space-filling) Curve was proposedin order to traverse triangular-shaped adaptive-refined meshes. Those curves are variations of the namesimilarwell-known space-filling curves, i.e. the Hilbert Curve and the Sierpi´nski Curve. Moreover, theyare adapted from those classical curves that traverse regular discretized domains. This paper describesthe asymptotic tight bounds of algorithms that update the Sierpi´nski-like and the Modified Hilbert Curvesspace-filling curves