Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mixing Time of Markov chain of the Knapsack Problem   To find the number of assignments of zeros and ones satisfying a specific
Knapsack Problem is $\#P$ hard, so only approximations are envisageable. A
Markov chain allowing uniform sampling of all possible solutions is given by
Luby, Randall and Sinclair. In 2005, Morris and Sinclair, by using a flow
argument, have shown that the mixing time of this Markov chain is
$\mathcal{O}(n^{9/2+\epsilon})$, for any $\epsilon > 0$. By using a canonical
path argument on the distributive lattice structure of the set of solutions, we
obtain an improved bound, the mixing time is given as $\tau_{_{x}}(\epsilon)
\leq n^{3} \ln (16 \epsilon^{-1})$.

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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
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The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an