Pii: 0020-0190(89)90045-8

Approximating the Diameter of a Set of Points in the Euclidean Space

Given a set P with n points in R , its diameter, dP , is the maximum of the Euclidean distances between its points. We describe an algorithm that in m ≤ n iterations obtains r1 < r2 < . . . < rm ≤ dP ≤ min { √3 r1 , √  5 − 2 √3 rm } . For k fixed, the cost of each iteration is O(n) . In particular in the first iteration, the algorithm produces an approximation r1 which is within √3 of d...

Optimal Three-Dimensional Layouts of Complete Binary Trees

We present optimal embeddings of an n-node complete binary tree in a three-dimensional or a two-dimensional grid when k, the size of one of the dimensions of the grid, is given. For the three-dimensional case we show how to obtain, for any k in the range [1, n/2], a layout of O(n+k logn) volume. The same bound is shown to hold for the two-dimensional case when k is in the range [log n , n/2]. W...

An Efficient Algorithm for Determining the Convex Hull of a Finite Planar Set

Step Find a point Pin the plane w%ch is in &he In&$x of Cl-l(s). At worst, this can be done in clfl sQp9 by te dting 3 element subsets of S for collineti@, discarding middle p&n& of collinear rets ar5b bq@rig when the fust noncollinear set (if there i# or&j. &y X, y arrcf z, is found. P can be chosen to I&E the centroid oC the triangle formed by X, y and z. Sfq 2: Express each si E S in polar c...

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The Behavior of Shared Objects: Concepts, Pitfalls, and a New Model