D S ] 2 2 O ct 2 00 4 Optimal Free-Space Management and Routing-Conscious Dynamic Placement for Reconfigurable Computers ∗

We describe algorithmic results on two crucial aspects of allocating resources on array-based hardware devices with partial reconfigurability. By using methods from the field of computational geometry, we derive a method that allows correct maintainance of free and occupied space of a set of n rectangular modules in time O(n log n); previous approaches needed a time of O(n) for correct results and O(n) for heuristic results. We also show a matching lower bound of Ω(n log n), so our approach is optimal. We also show that finding an optimal feasible communicationconscious placement (which minimizes the total weighted Manhattan distance between the new module and existing demand points) can be computed with Θ(n log n). Both resulting algorithms are practically easy to implement and show convincing experimental behavior. ACM Classification: C.1.3: Reconfigurable Hardware; F.2.2.c: Geometrical problems and computations