François Queyroi, Sergey Kirgizov
Information Processing Letters, Volume 115, Issue 9, September 2015, Pages 689–693 http://www.sciencedirect.com/science/article/pii/S0020019015000678
We discuss the computation of a distance between two hierarchical clusterings of the same set. It is defined as the minimum number of elements that have to be removed so the remaining clusterings are equal. The problem of distance computing was extensively studied for partitions. We prove it can be solved in polynomial time in the case of hierarchies as it gives birth to a class of perfect graphs. We also propose an algorithm based on recursively computing maximum assignments.