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Given a family of disjoint polygons P" P" . . . , Pk in the plane, and an integer parameter m, it is AT-complete to decide if the Pi's can be pairwise separated by a polygonal family with at most m edges, that is, if there exist polygons R" R" . . , R, with pairwise-disjoint boundaries such that Pi c Ri and C 1 Ri I< m. In three dimensions, the problem is NP-complete even for two . 0925-7721/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDIO925-7721(95)00006-2 96doi:10.1016/0925-7721(95)00006-u fatcat:wzf7ohyjerdmvjsxrdwkblb2ny