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This paper treats a loop pipeline scheduling problem under given resource assignment (operations to functional units and data to registers), which is one of the key tasks in design backtracking or in an assignment-driven approach for datapath synthesis. First we transform our scheduling problem into the problem of assigning integers to disjunctive arcs introduced to resolve lifetime collisions. After evaluating a feasible range of each variable to be fixed, we propose an heuristic method to reduce these ranges based on the sensitivity to iteration period so that every variable falls into an integer. Finally, our scheduler is incorporated into a Simulated Annealing exploration of assignment solution space, and data-path designs with an emphasis on connectivity minimization are demonstrated.