The combinatorial core of the OVSF code assignment problem that arises in UMTS is to assign some nodes of a complete binary tree of height h (the code tree) to n simultaneous connections, such that no two assigned nodes (codes) are on the same root-to-leaf path. Each connection requires a code on a specified level. The code can change over time as long as it is still on the same level. We consider the one-step code assignment problem: Given an assignment, move the minimum number of codes to serve a new request. Minn and Siu proposed the so-called DCAalgorithm to solve the problem optimally. We show that DCA does not always return an optimal solution, and that the problem is NP-hard. We give an exact nO(h)-time algorithm, and a polynomial time greedy algorithm that achieves approximation ratio Θ(h). Finally, we consider the online code assignment problem for which we derive several results
