A tree
and a value are given. An absolute quickest 1-center of tree is any point placed on nodes or edges of with the property that the transmission time to send units of data from the farthest node to is the minimum value. This paper defined a new inverse network location problem on a tree (called the inverse quickest center location problem), which changes the edge capacities with minimum total cost such that a given node becomes an absolute quickest 1-center. We consider two versions of the problem, where it is solved by decreasing and increasing edge capacities. First, two necessary and sufficient conditions for solving the problem are proved, then, two time algorithms to solve two versions of the problem are presented, where denotes the number of nodes.