Voronoi Diagram and Delaunay Triangulation: Applications and Challenges in Bioinformatics

This paper first covers the applications of Voronoi diagram and Delaunay triangulation based on the author's personal experience. On the successful part, it covers the history and development of the jump-and-walk algorithm, which is known as the first sublinear geometric algorithm nowadays and has been used in several famous software packages. On the bioinformatics applications, the paper focuses on three challenges: (1) contour interpolation, (2) protein folding, and (3) protein local structure alignment. Voronoi diagram and Delaunay triangulation plays important roles in handling these problems.