The topology diameters of the asymmetric cluster affinity cost

The asymmetric cluster affinity cost is based on the classic Robinson–Foulds metric and offers a more nuanced comparison of ordered tree pairs. When comparing the costs of these pairs, it is important to consider topology diameters to ensure a meaningful evaluation. The topology diameters of a cost represent the maximum values across all ordered tree pairs when the topology of either the first tree, the second tree, or both is fixed. This theoretical work outlines all topology diameters for the asymmetric cluster affinity cost and describes a linear-time algorithm that generates trees achieving the topology diameter for a given ordered pair of topologies. Our detailed experimental studies suggest that normalization strategies based on topology diameters can significantly improve comparative studies using the asymmetric cluster affinity cost.