Rigorous amortized-time analysis of the enumeration algorithms

Develop a rigorous amortized-time analysis of the enumeration algorithms introduced for generating weighted trees and weighted block trees, establishing precise bounds on their amortized running time.

Background

The authors provide experimental evidence suggesting their enumeration algorithms run in constant amortized time (CAT), drawing parallels to prior CAT algorithms for related tree classes, but they do not present a formal proof.

They explicitly state that a rigorous analysis of amortized enumeration time remains unresolved, highlighting the need for a formal treatment of amortized complexity for their enumeration procedures.

References

Enumerating weighted/block trees in some other order that will allow for sub-linear delay time and the rigorous analysis of the amortized enumeration time are left as open questions.

— Generation of weighted trees, block trees and block graphs  (2401.09764 - Ekim et al., 2024) in Section 7 (Conclusion), Future works