A tree T and a value σ are given. An absolute quickest 1-center of tree T is any point s∗ placed on nodes or edges of T with the property that the transmission time to send σ units of data from the farthest node to s∗ 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 s∗ 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 O (n) time algorithms to solve two versions of the problem are presented, where n denotes the number of nodes.
