A new staircase separator theorem

Abstract

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, rectangles into k subsets of (almost) equal size. We derive an optimal O(logn) 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 $\left\lceil {\frac{n}{2}} \right\rceil$, in compared to $\left\lceil {\frac{{7n}}{8}} \right\rceil$ in [2], on the quality of staircase separators for sets of rectangles.

work done while at Departement Informatik, ETH Zürich, Switzerland.

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