The Stretch Factor of $L_1$- and $L_\infty$-Delaunay Triangulations

The Stretch Factor of Hexagon-Delaunay Triangulations

The problem of computing the exact stretch factor (i.e., the tight bound on the worst case stretch factor) of a Delaunay triangulation has been open for more than three decades. Over the years, a series of upper and lower bounds on the exact stretch factor have been obtained but the gap between them is still large. An alternative approach to solving the problem is to develop techniques for comp...

The Stretch Factor of L 1- and L ∞ -Delaunay Triangulations

In this paper we determine the stretch factor of the L1-Delaunay and L∞-Delaunay triangulations, and we show that this stretch is √ 4 + 2 √ 2 ≈ 2.61. Between any two points x, y of such triangulations, we construct a path whose length is no more than

On the Dilation of Delaunay Triangulations of Points in Convex Position

Let S be a finite set of points in the Euclidean plane, and let E be the complete graph whose point-set is S. Chew, in 1986, proved a lower bound of π/2 on the stretch factor of the Delaunay triangulation of S (with respect to E), and conjectured that this bound is tight. Dobkin, Friedman, and Supowit, in 1987, showed that the stretch factor of the Delaunay triangulation of S is at most π( √ 5 ...

Toward the Tight Bound of the Stretch Factor of Delaunay Triangulations

In this paper, we investigate the tight bound of the stretch factor of the Delaunay triangulation by studying the stretch factor of the chain (Xia 2011). We define a sequence Γ = (Γ1,Γ2,Γ3, . . .) where Γi is the maximum stretch factor of a chain of i circles, and show that Γ is strictly increasing. We then present an improved lower bound of 1.5932 for the stretch factors of the Delaunay triang...

Contents The Stretch Factor of L 1 - and L ∞ - Delaunay Triangulations 3 The NOF Multiparty Communication Complexity of Composed Functions 3 Spectral Norm of Symmetric Functions