Maintaining centdians in a fully dynamic forest with top trees

In this paper, we consider the problem of maintaining the centdians in a fully dynamic forest. A forest is said to be fully dynamic if edge insertions, edge deletions, and changes of vertex weights are allowed. Centdian is a specific kind of facility that integrates the notions of center and median by taking a convex combination on the objective functions of both problems. This work extends the results in Alstrup et al. [2] within the same time complexity, i.e., linear time preprocessing and O(logn) per update, where n is the number of vertices of the components being updated.