Placing resources in a tree: Dynamic and static algorithms

We study the classical problem of optimally placing resources in a tree. We give dynamic algorithms that recompute the optimal solution after a weight change in polylogarithmic time for the case of one resource in a general tree and for any constant number of resources in a complete tree. Our algorithms are the first dynamic algorithms for this problem. We also give Linear-time algorithms for the static version of the problem for two resources. Previously known algorithms fun in time quadratic in the number of vertices. We also discuss an on-line amortized constant time algorithm for placing any number of resources on a line.