algorithms-optimization / Analysis of algorithms
Shellsort's worst-case running time is unknown for the gap sequences actually used in practice. Encoding a permutation as the polynomial $\sigma(1)z + \cdots + \sigma(n)z^n$ gives a framework for lower bounds, and yields $\Omega(N^{1.26})$ for Tokuda's 1992 sequence, extending to any strictly decreasing sequence staying within a fixed distance of a rational geometric one.
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a lower bound for Tokuda's sequence; the general Shellsort complexity question stays open
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Shellsort's worst-case running time is unknown for the gap sequences actually used in practice. Encoding a permutation as the polynomial $\sigma(1)z + \cdots + \sigma(n)z^n$ gives a framework for lower bounds, and yields $\Omega(N^{1.26})$ for Tokuda's 1992 sequence, extending to any strictly decreasing sequence staying within a fixed distance of a rational geometric one.
a lower bound for Tokuda's sequence; the general Shellsort complexity question stays open
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