A Depth - First Dynamic Programming Procedure forthe

The Extended Tree Knapsack Problem(ETKP) is a generalized version of the Tree Knapsack Problem where an arbitrary nonlinear traac-ow cost is imposed. This problem can be solved by the straightforward \bottom-up" approach with a time complexity of O(nH 2), where n is the number of nodes in the tree, and H is the knapsack capacity. In this paper, we show that if the traac-ow cost function is the cable expansion cost, which occurs in the Local Access Telecommunication Network (LATN) expansion, this special ETKP can be solved by a depth-rst dynamic programming procedure in a time complexity of O(nnH), where is the largest existing cable capacity in LATN. This result indicates that the depth-rst dynamic programming algorithm can be applied for solving a general class of tree optimization problems. The computational results of our algorithm for the ETKP are also provided.