Editor's foreword special issue on the sixth annual symposium on computational geometry

This special issue contains selected papers that are polished versions of results presented at the Sixth Annual Symposium on Computational Geometry, in Berkeley, California, June 6-8, 1990. In addition to their high technical quality, these papers have in common the feature that they belong to subareas of computational geometry that are attracting (or are likely to attract in the future) increasing interest in the community. The first paper, "Constructing Strongly Convex Hulls Using Exact or Rounded Arithmetic," by Zhenyu Li and Victor Milenkovic, is a significant step in the development of a theory of robust computational geometry. (Recall that robust algorithms are such that their correctness is not destroyed by roundoff error.) The paper gives algorithms for computing an e-strongly convex 6-hull of a set of points; this is a convex polygon P with vertices taken from the set of input points S, such that (i) no point of S lies farther than 6 outside P, and (ii) P remains convex even if the vertices of P are perturbed by as much as e. While solving this important specific problem, the paper develops techniques for dealing with approximate arithmetic in computational geometry. Since so many existing geometric algorithms misbehave if implemented with rounded arithmetic, we can expect an increase of activity in designing robust algorithms for geometric problems in the future. The next two papers introduce new algorithmic paradigms for dealing with complexity in computational geometry, and give appropriate notions of approximation that are appealing in that they capture intuitive notions of easiness and difficulty of a problem in more general ways than problem size, which is the more limited (and traditionally used) measure of these notions. In the paper "Simultaneous Inner and Outer Approximation of Shapes," by R. Fleischer, K. Mehlhorn, G. Rote, E. Welzl, and C. Yap, the slackness parameters of the input enable the development of algorithms that run faster by substituting simple objects for complex ones in the input, without destroying the practical acceptability of the resulting solution. In the paper "Approximate Motion Planning and the Complexity of the Boundary of the Union of Simple Geometric Figures," by H. Alt, R. Fleischer, M. Kaufmann, K. Mehlhorn, S. N/iher, S. Schirra, and C. Uhrig, the tightness of a motion planning problem enables the development of a faster algorithm than for the exact version of the problem, using a combinatorial