Partitioning Arrangements of Lines Ii Applications
Partitioning Arrangements of Lines Ii Applications
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In our eReader you can find the full English version of the book. Read Partitioning Arrangements of Lines Ii Applications 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 Partitioning Arrangements of Lines Ii Applications
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9 For each 1 < i < M, the number m, of lines passing through the cell Q, satisfies m, < max{2V2\/K + 4C, 2y/K + &(;}. (4. 8) Proof: Note that a cell Qi produced by our algorithm is a subset of some cell . F^ G F (the cells obtained by overlapping red, blue and green pseudo edges). Therefore it suffices to bound the number of lines passing through a cell in F. Fir st, let us consider a red-green cell ^ij = Qf n Q^. By Lemma 4. 5, Qf meets at most 2JKgg + 2^ green lines and Q^ meets at most 2\/Krr + 2^ red lines, and since no blue hne passes through a red-green cell, there are at most 2{\/KrT + jKgg -\- 2C, ) lines pass through . F, j. Similarly, we can show that a red-blue cell meets at most 2{\/Ktt + y/K^ + 2C) lines. Finally, let Tu be a red-blue-green cell, then Tu is the intersection of Qj, Q\ and Q\. Since Q\ (resp. Q\) meets at most 2^ green (resp. Blue) lines, Tu has at most 2\/Ktt + 6C Unes. Now the lemma follows from the fact that max{-yKV7 + \/i^66, >/^V7 + J^gg] ^ ^/2K. U For X, y G {r, 6, g], let cSf denote the nvunber of pseudo edges of color x intersected by the line U of color y.
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To quickly assess the difficulty of the text, read a short excerpt:
9 For each 1 < i < M, the number m, of lines passing through the cell Q, satisfies m, < max{2V2\/K + 4C, 2y/K + &(;}. (4. 8) Proof: Note that a cell Qi produced by our algorithm is a subset of some cell . F^ G F (the cells obtained by overlapping red, blue and green pseudo edges). Therefore it suffices to bound the number of lines passing through a cell in F. Fir st, let us consider a red-green cell ^ij = Qf n Q^. By Lemma 4. 5, Qf meets at most 2JKgg + 2^ green lines and Q^ meets at most 2\/Krr + 2^ red lines, and since no blue hne passes through a red-green cell, there are at most 2{\/KrT + jKgg -\- 2C, ) lines pass through . F, j. Similarly, we can show that a red-blue cell meets at most 2{\/Ktt + y/K^ + 2C) lines. Finally, let Tu be a red-blue-green cell, then Tu is the intersection of Qj, Q\ and Q\. Since Q\ (resp. Q\) meets at most 2^ green (resp. Blue) lines, Tu has at most 2\/Ktt + 6C Unes. Now the lemma follows from the fact that max{-yKV7 + \/i^66, >/^V7 + J^gg] ^ ^/2K. U For X, y G {r, 6, g], let cSf denote the nvunber of pseudo edges of color x intersected by the line U of color y.
What to read after Partitioning Arrangements of Lines Ii Applications?
You can find similar books in the "Read Also" column, or choose other free books by Pankaj K Agarwal to read online
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