The inverse center subtree problem on tree graphs

A center subtree is a subtree with a specified length that minimizes the maximum weighted distance between the vertices in a network and the subtree. This paper addresses the inverse center subtree problem on tree graphs, where vertex weights are adjusted to either augment or reduce them, aiming to transform a predetermined subtree into a center subtree. Initially, we explore the optimality criterion for a subtree that is a center subtree within a tree network. Using this criterion, we frame the corresponding problem as a piecewise linear optimization problem. Lastly, we propose a combinatorial algorithm that effectively solves the problem in [Formula: see text] time, where [Formula: see text] represents the number of vertices in the tree.