An Introduction to Randomized algorithms - School of Technology ...
An Introduction to Randomized algorithms - School of Technology ...
An Introduction to Randomized algorithms - School of Technology ...
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
Verifying matrix multiplication :A, B, C ∈ F n×n ; Goal : To verify if AB = C.direct approach - O(n 3 ) time.algebraic approach - O(n 2.376 ) time.<strong>Randomized</strong> Alg :Choose u.a.r. r ∈ {0, 1} n and check if ABr = Cr.If so, output YES, otherwise output NO.If AB ≠ C, then Pr(ABr = Cr) ≤ 1/2.requires O(n 2 ) time.<strong>An</strong> example <strong>of</strong> a Monte-Carlo algorithm : can be incorrect butguaranteed running time and with a guarantee <strong>of</strong> confidence.
Change language