The random graph revisited

The Random Graph Revisited

Bertrand’s Paradox Revisited: More Lessons about that Ambiguous Word, Random

The Bertrand paradox question is: “Consider a unit-radius circle for which the length of a side of an inscribed equilateral triangle equals 3 . Determine the probability that the length of a ‘random’ chord of a unit-radius circle has length greater than 3 .” Bertrand derived three different ‘correct’ answers, the correctness depending on interpretation of the word, random. Here we employ geomet...

QUICKSELECT Revisited

We give an overview of the running time analysis of the random divide-and-conquer algorithm FIND or QUICKSELECT. The results concern moments, distribution of FIND’s running time, the limiting distribution, a stochastic bound and the key: a stochastic fixed point equation.

Sweep Line Algorithm for Convex Hull Revisited

Convex hull of some given points is the intersection of all convex sets containing them. It is used as primary structure in many other problems in computational geometry and other areas like image processing, model identification, geographical data systems, and triangular computation of a set of points and so on. Computing the convex hull of a set of point is one of the most fundamental and imp...

Random cubic planar graphs revisited