TEL-AVIV UNIVERSITY RAYMOND AND BEVERLY SACKLER FACULTY OF EXACT SCIENCES BLAVATNIK SCHOOL OF COMPUTER SCIENCE Counting Triangulations of Planar Point Sets
نویسنده
چکیده
We study the maximal number of triangulations that a planar set of n points can have, and show that it is at most 30n. This new bound is achieved by a careful optimization of the charging scheme of Sharir and Welzl (2006), which has led to previous best upper bound of 43n for the problem. Moreover, this new bound is useful for bounding the number of other types of planar (i.e., crossing free) straight-line graphs on a given point set. Specifically, we derive new upper bounds for the number of planar graphs (o (239.4n)), spanning cycles (O(70.21n)), and spanning trees (160n).
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School of Computer Science, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel Department of Biopharmaceutical Sciences and Pharmaceutical Chemistry, and California Institute for Quantitative Biomedical Research, University of California at San Francisco, San Francisco, CA 94158, USA School of Crystallography, Birkbeck College University of London...
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