Sub-linear delay enumeration order for weighted trees and weighted block trees

Determine whether there exists an enumeration order for generating weighted trees and weighted block trees that achieves sub-linear output delay time between consecutive outputs, where delay is measured as a function of the size of the emitted tree.

Background

The paper develops enumeration and unranking algorithms for rooted and free trees, extends them to non-negatively weighted trees, and applies the framework to weighted block trees to enumerate connected block graphs. The authors analyze output delay time and show that their enumeration algorithms have linear output delay complexity.

They suggest that reordering the enumeration might improve delay further and explicitly identify the existence of an order achieving sub-linear delay for weighted and block trees as an unresolved question.