Expected Parallel Time And Sequential Space Complexity of Graph And Digraph Prob
Expected Parallel Time And Sequential Space Complexity of Graph And Digraph Prob
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1. At the end of (a) of phase i of stage 2, each large super- vertex has size at least s(i)/(6 log n) .
We now will show LEMMA 3. 1. If a supervertex has size ^s(i), then it is declared large idth -(S-1) probability at least 1-n -15- Proof. Let p(i) be the number of cells of the table of the supervertex, which stay at value after (a) of stage 2. We know that s(i) is increasing with 4 i and s (1) is 21og n. The probability that the particular supervertex fails to be declared large is prob{There ...is a particular memory cell staying at value 0} = (l-l/(s(i)/(B log n)))"^^' ^ e"^' ^°^ " so prob{p(i) = O} ^ n-n = n "" o -2 We now inductively assume that for iJJl, with probability >l-n, "At least — r nodes are in large supervertices" . The basis, i = l, was proved previously.
2^ Let N. Be the number of large supervertices at end of (a) of phase i.
Fact 1 . For any n, p, 3 with n>0, l^p>0 and
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To quickly assess the difficulty of the text, read a short excerpt:
1. At the end of (a) of phase i of stage 2, each large super- vertex has size at least s(i)/(6 log n) .
We now will show LEMMA 3. 1. If a supervertex has size ^s(i), then it is declared large idth -(S-1) probability at least 1-n -15- Proof. Let p(i) be the number of cells of the table of the supervertex, which stay at value after (a) of stage 2. We know that s(i) is increasing with 4 i and s (1) is 21og n. The probability that the particular supervertex fails to be declared large is prob{There ...is a particular memory cell staying at value 0} = (l-l/(s(i)/(B log n)))"^^' ^ e"^' ^°^ " so prob{p(i) = O} ^ n-n = n "" o -2 We now inductively assume that for iJJl, with probability >l-n, "At least — r nodes are in large supervertices" . The basis, i = l, was proved previously.
2^ Let N. Be the number of large supervertices at end of (a) of phase i.
Fact 1 . For any n, p, 3 with n>0, l^p>0 and
What to read after Expected Parallel Time And Sequential Space Complexity of Graph And Digraph Prob?
You can find similar books in the "Read Also" column, or choose other free books by John Reif to read onlineMoreLess
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