Multiple covers with balls I: Inclusion-exclusion
نویسندگان
چکیده
Inclusion-exclusion is an effective method for computing the volume of a union of measurable sets. We extend it to multiple coverings, proving short inclusion-exclusion formulas for the subset of R covered by at least k balls in a finite set. We implement two of the formulas in dimension n = 3 and report on results obtained with our software.
منابع مشابه
P´olya-Type Urn Models with Multiple Drawings
We investigate the distribution, mean value, variance and some limiting properties of an urn model of white and red balls under random multiple drawing (either with or without replacement) when the number of white and red balls added follows a schedule that depends on the number of white balls chosen in each drawing.
متن کاملMultiple Covers with Balls II: Weighted Averages
Voronoi diagrams and Delaunay triangulations have been extensively used to represent and compute geometric features of point configurations. We introduce a generalization to poset diagrams and poset complexes, which contain order-k and degree-k Voronoi diagrams and their duals as special cases. Extending a result of Aurenhammer from 1990, we show how to construct poset diagrams as weighted Voro...
متن کاملCryogenic Milling of Titanium Powder
Ti Grade 2 was prepared by cryogenic attritor milling in liquid nitrogen and liquid argon. Two types of milling balls were used—stainless steel balls and heavy tungsten carbide balls. The effect of processing parameters on particle size and morphology, contamination of powder and its microhardness was investigated. Milling in liquid nitrogen was not feasible due to excessive contamination by ni...
متن کاملThe Inclusion-Exclusion Principle for IF-States
Applying two definitions of the union of IF-events, P. Grzegorzewski gave two generalizations of the inclusion-exclusion principle for IF-events.In this paper we prove an inclusion-exclusion principle for IF-states based on a method which can also be used to prove Grzegorzewski's inclusion-exclusion principle for probabilities on IF-events.Finally, we give some applications of this principle by...
متن کاملImproved Inclusion-exclusion Inequalities for Simplex and Orthant Arrangements
Improved inclusion-exclusion inequalities for unions of sets are available wherein terms usually included in the alternating sum formula can be left out. This is the case when a key abstract tube condition, can be shown to hold. Since the abstract tube concept was introduced and refined by the authors, several examples have been identified, and key properties of abstract tubes have been describ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Comput. Geom.
دوره 68 شماره
صفحات -
تاریخ انتشار 2018