The k-Robinson-Foulds Dissimilarity Measures for Comparison of Labeled Trees

Understanding the mutational history of tumor cells is a critical endeavor in unraveling the mechanisms underlying cancer. Since the modeling of tumor cell evolution employs labeled trees, researchers are motivated to develop different methods to assess and compare mutation trees and other labeled trees. While the Robinson-Foulds distance is a widely utilized metric for comparing phylogenetic trees, its applicability to labeled trees reveals certain limitations. This paper introduces the $k$-Robinson-Foulds dissimilarity measures, tailored to address the challenges of labeled tree comparison. The Robinson-Foulds distance is succinctly expressed as n-RF in the space of labeled trees with n nodes. Like the Robinson-Foulds distance, the k-Robinson-Foulds is a pseudometric for multiset-labeled trees and becomes a metric in the space of 1-labeled trees. By setting k to a small value, the k-Robinson-Foulds dissimilarity can capture analogous local regions in two labeled trees with different size or different labels.