A New Staircase Separator Theorem ? Viet

The notion of staircase separator, introduced in 2], greatly facilitates the design of divide-and-conquer algorithms for problems on rectangles. We generalize the concept of staircase separator to k-perfect staircase separator, namely a set of staircase separators which partitions a set S of n axis-parallel, disjoint rectangles into k subsets of (almost) equal size. We derive an optimal O(log n) time parallel algorithm for computing a k-perfect staircase separator, using O(n) processors on the CREW PRAM model of computation. For a special case, where k = 2, this result provides a new bound of d n 2 e, in compared to d 7n 8 e in 2], on the quality of staircase separators for sets of rectangles.