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- W2952159740 abstract "Given a weighted $n$-vertex graph $G$ with integer edge-weights taken from a range $[-M,M]$, we show that the minimum-weight simple path visiting $k$ vertices can be found in time $tilde{O}(2^k poly(k) M n^omega) = O^*(2^k M)$. If the weights are reals in $[1,M]$, we provide a $(1+varepsilon)$-approximation which has a running time of $tilde{O}(2^k poly(k) n^omega(loglog M + 1/varepsilon))$. For the more general problem of $k$-tree, in which we wish to find a minimum-weight copy of a $k$-node tree $T$ in a given weighted graph $G$, under the same restrictions on edge weights respectively, we give an exact solution of running time $tilde{O}(2^k poly(k) M n^3) $ and a $(1+varepsilon)$-approximate solution of running time $tilde{O}(2^k poly(k) n^3(loglog M + 1/varepsilon))$. All of the above algorithms are randomized with a polynomially-small error probability." @default.
- W2952159740 created "2019-06-27" @default.
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- W2952159740 date "2013-07-09" @default.
- W2952159740 modified "2023-09-27" @default.
- W2952159740 title "Finding the Minimum-Weight k-Path" @default.
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