Fused trees and some new approaches to source coding

The concept of fusion partition for the node set of a tree, and the concept of a fused tree corresponding to it, are discussed. A fused tree requires, in principle, significantly less memory for storage than the original tree yet allows the recovery of the original. Hence, it makes sense to store a tree in a fused form. Furthermore, if labels from an ordered set C are assigned to the branches of the original tree so that a lexographic (alphabetic) order on the set of terminal nodes is induced, a fused tree still enables the execution of direct and inverse enumeration algorithms. A fusion algorithm to produce the completely fused tree for a given tree is presented. Some approaches to data compression problems related to the algorithms given are discussed