Amortized Analysis on Enumeration Algorithms

Years and Authors of Summarized Original Work

• 1998; Uno

Problem Definition

Let $\mathcal{A}$ be an enumeration algorithm. Suppose that $\mathcal{A}$ is a recursive type algorithm, i.e., composed of a subroutine that recursively calls itself several times (or none). Thus, the recursion structure of the algorithm forms a tree. We call the subroutine or the execution of the subroutine an iteration. We here assume that an iteration does not include the computation done in the recursive calls generated by itself. We regard a series of subroutines of different types as an iteration if they form a nested recursion. We simply write the set of all iterations of an execution of $\mathcal{A}$ by $\mathcal{X}$.

When an iteration X recursively calls an iteration Y, X is called the parent of Y, and Y is called a child of X. The root iteration is that with no parent. For non-root iteration X, its parent is unique and is denoted by P(X). The set of the children of X is denoted by C(X). The...