6203082
Area and Perimeter Derivatives of a Union of Disks
We give analytic inclusion-exclusion formulas for the area and perimeter derivatives of a union of finitely many disks in the plane.
33621218
Superimposing Voronoi Complexes for Shape Deformation
Edelsbrunner et al. defined a framework of shape deformations with shapes bounded by skin manifold. We prove that the infinitely many synthesized shapes in the deformation sequence share finitely many common Voronoi complexes. Therefore, we propose a new algorithm to compute the common Voronoi complexes efficiently for the deformations, and use these common complexes to compute the synthesized shapes in real time. This makes generating, visualizing, and customizing shape deformations feasible.
46280169
Edge-gracefulness of the composition of paths with null graphs
Let G = (V,E) be a (p,q)-graph. Let f:E → {1,2,..., q} be a bijection. The induced mapping f+ : V → Zp of f is defined by f+(u) ≡ Σuυ∈Ef(uυ) (modp) for u ∈ V. If f+ is a bijection, then G is called edge-graceful. In this paper, we investigate the edge-gracefulness of the composition of paths with null graphs Pm > Nn, where there are mn vertices and (m - 1)n2 edges. We show that P3 > Nn is edge-graceful if n is odd.
14350917
A non-linear dimensionality-reduction technique for fast similarity search in large databases
To enable efficient similarity search in large databases, many indexing techniques use a linear transformation scheme to reduce dimensions and allow fast approximation. In this reduction approach the approximation is unbounded, so that the approximation volume extends across the dataspace. This causes over-estimation of retrieval sets and impairs performance.This paper presents a non-linear transformation scheme that extracts two important parameters specifying the data. We prove that these parameters correspond to a bounded volume around the search sphere, irrespective of dimensionality. We use a special workspace-mapping mechanism to derive tight bounds for the parameters and to prove further results, as well as highlighting insights into the problems and our proposed solutions. We formulate a measure that lower-bounds the Euclidean distance, and discuss the implementation of the technique upon a popular index structure. Extensive experiments confirm the superiority of this technique over recent state-of-the-art schemes.