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• W2051236701 abstract "We investigate asymptotically the expected number of steps taken by backtrack search for k-coloring random graphs Gn,p(n) or proving non-k-colorability, where p(n) is an arbitrary sequence tending to 0, and k is constant. Contrary to the case of constant p, where the expected runtime is known to be O(1), we prove that here the expected runtime tends to infinity. We establish how the asymptotic behavior of the expected number of steps depends on the sequence p(n). In particular, for p(n)=d/n, where d is a constant, the runtime is always exponential, but it can be also polynomial if p(n) decreases sufficiently slowly, e.g. for p(n)=1/lnn." @default.
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• W2051236701 date "2013-12-01" @default.
• W2051236701 modified "2023-10-18" @default.
• W2051236701 title "Average-case complexity of backtrack search for coloring sparse random graphs" @default.
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• W2051236701 doi "https://doi.org/10.1016/j.jcss.2013.06.003" @default.
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