**Edge insertion for optimal triangulations**.

M. Bern, H. Edelsbrunner, D. Eppstein, S. Mitchell, and T.S. Tan.

*1st Latin Amer. Symp. Theoretical Informatics,*Sao Paulo, 1992.

Springer,*Lecture Notes in Comp. Sci.*583, 1992, pp. 46–60.

Tech. Rep. EDC UILU-ENG-92-1702, Univ. Illinois, Urbana-Champaign, 1992.

*Disc. & Comp. Geom.*10: 47–65, 1993.One standard way of constructing Delaunay triangulations is by iterated local improvement, in which each step flips the diagonal of some quadrilateral. For many other optimal triangulation problems, flipping is insufficient, but the problems can instead be solved by a more general local improvement step in which a new edge is added to the triangulation, cutting through several triangles, and the region it cuts through is retriangulated on both sides.

(BibTeX – Citations – CiteSeer – ACM DL)

**Application Challenges to Computational Geometry**.

The Computational Geometry Impact Task Force Report.

Tech. Rep. TR-521-96, Princeton University, April 1996.

Advances in Discrete and Computational Geometry – Proc. 1996 AMS-IMS-SIAM Joint Summer Research Conf. Discrete and Computational Geometry: Ten Years Later, Contemporary Mathematics 223, Amer. Math. Soc., 1999, pp. 407–423.**Emerging challenges in computational topology**.

M. Bern, D. Eppstein, et al.

arXiv:cs.CG/9909001.

This is the report from the ACM Workshop on Computational Topology run by Marshall and myself in Miami Beach, June 1999. It details goals, current research, and recommendations in this emerging area of collaboration between computer science and mathematics.

(BibTeX – Citations – CiteSeer)

Co-authors – Publications – David Eppstein – Theory Group – Inf. & Comp. Sci. – UC Irvine

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