کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6424509 | 1343400 | 2012 | 7 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Piercing quasi-rectangles-On a problem of Danzer and Rogers
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
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چکیده انگلیسی
It is an old problem of Danzer and Rogers to decide whether it is possible to arrange O(1ε) points in the unit square so that every rectangle of area ε>0 within the unit square contains at least one of them. We show that the answer to this question is in the negative if we slightly relax the notion of rectangles, as follows.Let δ be a fixed small positive number. A quasi-rectangle is a region swept out by a continuously moving segment s, with no rotation, so that throughout the motion the angle between the trajectory of the center of s and its normal vector remains at most δ. We show that the smallest number of points needed to pierce all quasi-rectangles of area ε>0 within the unit square is Î(1εlog1ε).
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Combinatorial Theory, Series A - Volume 119, Issue 7, October 2012, Pages 1391-1397
Journal: Journal of Combinatorial Theory, Series A - Volume 119, Issue 7, October 2012, Pages 1391-1397
نویسندگان
János Pach, Gábor Tardos,