Using the WSPD construction, we can easily compute an ε-approximation to the diameter of a point set Pin linear time. Given ε, we let s= 4/εand construct an s-WSPD. As mentioned above, each pair (P(u),P(v)) in our WSPD construction consists of the points descended from two nodes, uand v, in a compressed quadtree.

Callahan and Kosaraju [8, 10] devised the well-separated pair decomposition (WSPD), and showed that it can be used to solve a large variety of distance problems. Intuitively, a WSPD is a partition of the n 2 edges of the complete Euclidean graph into O(n) subsets. Each subset in this partition is represented by

Introduced by Callahan and Kosaraju back in 1995, the concept of well-separated pair decomposition (WSPD) has occupied a special significance in computational geometry when it comes to solving distance problems in d-space. We present an in-browser tool that can be used to visualize WSPDs and several of their applications in 2-space.

2022年5月9日 · Introduced by Callahan and Kosaraju back in 1995, the concept of well-separated pair decomposition (WSPD) has occupied a special significance in computational geometry when it comes to solving distance problems in -space. We present an in-browser tool that can be used to visualize WSPDs and several of their applications in -space.

Pu, Pv} output by the algWSPD algorithm. Note that algWSPD always stops if both u and v are leafs, whic. , then α = max(diam(Pu), diam(Pv)) > 0. This implies that d(Pu, Pv) ≥ d(u, v) ≥ ∆(u)/�. ≥ α/ε > d(Pu, Pv) ≤ d(q. s), since P. (u) < ∆(p(u)) and ∆(v) < ∆(p(v)). The idea is to track the pairs used in the recursive calls to .

2024年12月1日 · We present a memoryless local routing algorithm for heavy path WSPD spanners. The routing algorithm requires a vertex v of the graph to store O (deg ⁡ (v) log ⁡ n) bits of information, where deg ⁡ (v) is the degree of v. The routing ratio is at most 1 + 4 / s + 1 / (s − 1) and at least 1 + 4 / s in the worst case.

Accordingly, a surface duct (SD) is virtually ubiquitous with its depth compared with the MIBL depth. The wind direction and the SD characteristics exhibit diurnal variations over the SCB area ...

Trivially, there exists a WSPD of size O(n2) by setting the fA i;B igpairs to each of the distinct pair singletons of P. Our goal is to show that, given an n-element point set P in Rd and any s > 0, there exists a s-WSPD of size O(n) (where the constant depends on s and d).

In this lecture, we discuss WSPD, a data structure for organizing multi-dimensional points with a tunable scaling parameter s, which allows us to solve many higher di- mensional problems in almost linear time with approximation controlled by parameter

Dr. Tamara Mchedlidze Dr. Darren Strash Computational Geometry Lecture Applications of WSPD & Visibility Graphs 7 Discussion What are further applications of the WSPD? WSPD is useful whenever one can do without knowing all ( n2) exact distances in a point set and approximate them instead. One example are