Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  addresses the problem of pairwise comparisons in spectral ranking from an ordinary differential equation view. Given a nonnegative symmetric matrix    A      A        of order  n   ,  provide an   O(1)     O  (  1  )        algorithm for single pairwise comparison without computing the exact value of the principal eigenvector of    A      A        if assuming    A      A        and    A  2        A    2          have been constructed offline, which further leads to an   O(ν 2 )     O  (    ν    2    )        algorithm for ranking any subset of size  ν   , or an   O( kn )     O  (  kn  )        algorithm for the top  k  selection.  prove that in ER graphs the correct rate of pairwise comparisons converges to one as  n  approaches infinity.  also experimentally demonstrate the high correct rate on various artificial and real-world graphs.
['Ying Tang', 'Yinrun Li']
I am writing a research paper on a idea Pairwise comparisons in spectral ranking
[{"from": "human", "value": "I am writing a research paper on a idea Pairwise comparisons in spectral ranking"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  addresses the problem of pairwise comparisons in spectral ranking from an ordinary differential equation view. Given a nonnegative symmetric matrix    A      A        of order  n \u00a0 ,  provide an   O(1)     O  (  1  )        algorithm for single pairwise comparison without computing the exact value of the principal eigenvector of    A      A        if assuming    A      A        and    A  2        A    2          have been constructed offline, which further leads to an   O(\u03bd 2 )     O  (    \u03bd    2    )        algorithm for ranking any subset of size  \u03bd \u00a0 , or an   O( kn )     O  (  kn  )        algorithm for the top  k  selection.  prove that in ER graphs the correct rate of pairwise comparisons converges to one as  n  approaches infinity.  also experimentally demonstrate the high correct rate on various artificial and real-world graphs."}]