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- W312324576 abstract "Consider the random n <TEX>$times$</TEX> m assignment problem with m <TEX>$geq$</TEX> <TEX>$_{i,j}$</TEX> Let <TEX>$u_{i,j}$</TEX> be iid uniform random variables on [0, 1] and exponential random variables with mean 1, respectively, and let <TEX>$U_{n, m}$</TEX> and <TEX>$T_{n, m}$</TEX> denote the optimal assignment costs corresponding to <TEX>$u_{i, j}$</TEX> and <TEX>$t_{i, j}$</TEX>. In this paper we first give a comparison result about the discrepancy E <TEX>$T_{n, m}$</TEX> -E <TEX>$U_{n, m}$</TEX>. Using this comparison result with a known lower bound for Var( <TEX>$T_{n, m}$</TEX>) we obtains a lower bound for Var( <TEX>$U_{n, m}$</TEX>). Finally, we study the way that E <TEX>$U_{n, m}$</TEX> and E <TEX>$T_{n, m}$</TEX> vary as m does. It turns out that only when m - n is large enough, the cost decreases significantly.tly." @default.
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- W312324576 date "2002-10-01" @default.
- W312324576 modified "2023-09-25" @default.
- W312324576 title "ON THE RANDOM n×n ASSIGNMENT PROBLEM" @default.
- W312324576 cites W1980848544 @default.
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- W312324576 doi "https://doi.org/10.4134/ckms.2002.17.4.719" @default.
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