The assignment problem originally arising from parallel and distributed computing has been investigated intensively since the 70?s when Harold Stone proposed a method to solve it with the aid of network flow algorithms. In this paper, we discuss this problem under a mobile environment with limited capacity of wireless links. The assignment problem is to schedule a group of related objects from a resource-constrained mobile device to its powerful proxy machine so that program activity migrates among processors as execution proceeds, and hence the overall performance will improve. First, we reduce this optimization problem to the 0/1 Knapsack Problem, and therefore show that it is NP-hard. Second, two heuristic algorithms are proposed. One is an adaptive heuristic algorithm with complexity O(NE), here, N and E represent the number of nodes and edges in the object graph abstracted from the mobile application. The other is a non-adaptive heuristic algorithm with complexity O(E), i.e, N times faster than the adaptive counterpart. Finally, we provide a simple distributed algorithm based on Raymond?s tree-based distributed mutual exclusion algorithm for solving this problem with message complexity O(N 2 logN).