Very Fast Algorithms for the Area of the Union of Many Circles
Very Fast Algorithms for the Area of the Union of Many Circles
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In our eReader you can find the full English version of the book. Read Very Fast Algorithms for the Area of the Union of Many Circles Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Very Fast Algorithms for the Area of the Union of Many Circles
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■ r. L- --. '-^ . :. !
-7- 2. 3. 2. The straightforward approach Let us assume that we can find (in time a(n)) a closed curve A (enclosing area E(A)), which completely encloses the n circles. Assume also that we have a fast way (of time T(n) per point selection) of selecting points within A (or the interior of A) in a uniformly random manner (meaning that the probability of a point selected to fall Into an elementary area, Ae, around a specific point Pq, is the same VP^ (A plus interior (A)) an...d it is equal to • Ae. ) E(A) Finally, let 3(n) be the time it takes to decide if a given (arbitrarily selected) point P belongs to the union of the n circles.
Straightforward MC 1 E( A) (I) We select N > [ - ij points, uniformly randomly.
(Note that, to do this selection we don't need to know U, just an upper bound on E(A)/U is sufficient).
(II) For each point selected in (I), we test if it belongs to the union of circles. Let M
What to read after Very Fast Algorithms for the Area of the Union of Many Circles?
You can find similar books in the "Read Also" column, or choose other free books by Paul G Spirakis to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
■ r. L- --. '-^ . :. !
-7- 2. 3. 2. The straightforward approach Let us assume that we can find (in time a(n)) a closed curve A (enclosing area E(A)), which completely encloses the n circles. Assume also that we have a fast way (of time T(n) per point selection) of selecting points within A (or the interior of A) in a uniformly random manner (meaning that the probability of a point selected to fall Into an elementary area, Ae, around a specific point Pq, is the same VP^ (A plus interior (A)) an...d it is equal to • Ae. ) E(A) Finally, let 3(n) be the time it takes to decide if a given (arbitrarily selected) point P belongs to the union of the n circles.
Straightforward MC 1 E( A) (I) We select N > [ - ij points, uniformly randomly.
(Note that, to do this selection we don't need to know U, just an upper bound on E(A)/U is sufficient).
(II) For each point selected in (I), we test if it belongs to the union of circles. Let M
What to read after Very Fast Algorithms for the Area of the Union of Many Circles?
You can find similar books in the "Read Also" column, or choose other free books by Paul G Spirakis to read onlineMoreLess
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