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Abstract. Given a set P of red points and a set Q of blue points in a plane with total size n, we investigate the problem of nding two disjoint isothetic rectangles containing all the points of Q, avoiding any points of P . Such rectangles are called two separating disjoint isothetic rectangles. We rst compute two separating disjoint axisaligned rectangles in O(n log n) time. Then, we relax the axis-aligned constraint and report all combinatorially di erent two separating disjoint isothetic rectangles. To compute these rectangles, we introduce some events by rotating the coordinate system and processing these events. Computing and processing all of the events are done in O(n 2 log n) time. Thus, our algorithm reports all combinatorially di erent separating rectangles in O(n 2 log n) time.

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Given a set P of red points and a set Q of blue points in the plane, of total size n, we investigate the problem of finding triangles with a given angle [Formula: see text] that (a) contain all points of Q, (b) avoid all points of P, and (c) are minimal, i.e. their three sides are tangent to the convex hull of Q. Such triangles are called minimal separating [Formula: see text]-triangles. We give an algorithm for reporting all combinatorially different minimal separating [Formula: see text]-triangles in [Formula: see text] time.