Nonexhaustive Generalized Fibonacci Trees in Unequal Costs Coding Problems

In a sequence of generalized Fibonacci trees, the kth tree has the (k c(i))th tree as its ith subtree for a nondecreasing sequence of positive integers c(i), i = 1; :::; r. For particular initializations, each tree in the generalized Fibonacci sequence solves a minimax coding problem related to Varn coding. Speci cally, each symbol from a uniformly distributed source is to be encoded by a string of code symbols associated with the path through the tree from the root to the leaf associated with the source symbol, the ith code symbol costs c(i), and the goal is to minimize maximum codeword cost.