An efficient algorithm for finding empty space for online FPGA placement

Abstract

A fast and efficient algorithm for finding empty area is necessary for online placement, task relocation and defragmentation on a partially reconfigurable FPGA. We present an algorithm that finds empty area as a list of overlapping maximal rectangles. Using an innovative representation of the FPGA, we are able to predict possible locations of the maximal empty rectangles. Worst-case time complexity of our algorithm is O(xy) where x is the number of columns, y is the number of rows and x.y is the total number of cells on the FPGA. Experiments show that, in practice, our algorithm needs to scan less than 15% of the FPGA cells to make a list of all maximal empty rectangles.