We analyse the average number of buckets in a Linear Bucket tree created by n points uniformly dispatched on an interval of length y. A new bucket is created when a point does not fall in an existing bucket. The bucket is the interval of length 2 centered on the point. We illustrate this concept by an interesting tale of how the moon’s surface took on its present form. Thanks to an explicit Lap...

We study the broadcasting problem when underlying tree is a random recursive tree. The root of has bit value assigned. Every other vertex same as its parent with probability 1?q and opposite q, where q?[0,1]. consists in estimating upon observing unlabeled tree, together associated every vertex. In more difficult version problem, observed but only values leaves are observed. When uniform both v...