An Asynchronous Parallel Algorithm for Undirected Graph Connectivity
An Asynchronous Parallel Algorithm for Undirected Graph Connectivity
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In our eReader you can find the full English version of the book. Read An Asynchronous Parallel Algorithm for Undirected Graph Connectivity 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 An Asynchronous Parallel Algorithm for Undirected Graph Connectivity
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O Lemma 6. 4 For any pair of vertices u and v, and for any step number, ti, if u and v are in the same component of Gf^ then they are in the same component of Gf^ for any ^i • Proof. The proof is by induction on the step number. Initially the lemma holds. Assume the lemma holds at step f for aH f t". Likewise, w = next, (v), and Ff>{w) are in the same component of Gt"', for t'" > t". Finally, w and v are in the same component of Gf by definition, and hence of Gp, for t"' > t", by Lemma 6. 4. C...learly the inductive hypothesis holds for f = t" + 1; so the lemma follows by induction.
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To quickly assess the difficulty of the text, read a short excerpt:
O Lemma 6. 4 For any pair of vertices u and v, and for any step number, ti, if u and v are in the same component of Gf^ then they are in the same component of Gf^ for any ^i • Proof. The proof is by induction on the step number. Initially the lemma holds. Assume the lemma holds at step f for aH f t". Likewise, w = next, (v), and Ff>{w) are in the same component of Gt"', for t'" > t". Finally, w and v are in the same component of Gf by definition, and hence of Gp, for t"' > t", by Lemma 6. 4. C...learly the inductive hypothesis holds for f = t" + 1; so the lemma follows by induction.
What to read after An Asynchronous Parallel Algorithm for Undirected Graph Connectivity?
You can find similar books in the "Read Also" column, or choose other free books by Richard Cole to read onlineMoreLess
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