Tree evolution processes for bucket increasing trees

Geometric Bucket Trees: Analysis of Linear Bucket Tree

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...

Fried Chicken Bucket Processes

Chinese restaurant processes are useful hierarchical models; however, they make certain assumptions on finiteness that may not be appropriate for modeling some phenomena. Therefore, we introduce fried chicken bucket processes (FCBP) that involve different sampling methods. We also introduce spork notation as a simple way of representing this model.

Bucket Errors in MBE Trees

Bucket-Tree Elimination for Automated Reasoning

The paper extends several variable elimination schemes into a two-phase message passing algorithm along a bucket-tree. Our analysis shows that the new algorithm, called Bucket-Tree Elimination (BTE), may provide a substantial speed-up over standard variable-elimination for important probabilistic reasoning tasks. The algorithm is developed and analyzed within a unifying view of tree-clustering ...

On the Multiplicative Zagreb Indices of Bucket Recursive‎ ‎Trees

‎Bucket recursive trees are an interesting and natural‎ ‎generalization of ordinary recursive trees and have a connection‎ to mathematical chemistry‎. ‎In this paper‎, ‎we give the lower and upper bounds for the moment generating‎ ‎function and moments of the multiplicative Zagreb indices in a‎ ‎randomly chosen bucket recursive tree of size $n$ with maximal bucket size $bgeq1$‎. Also, ‎we consi...