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- W4387432217 abstract "The greedy and nearest-neighbor TSP heuristics can both have $log n$ approximation factors from optimal in worst case, even just for $n$ points in Euclidean space. In this note, we show that this approximation factor is only realized when the optimal tour is unusually short. In particular, for points from any fixed $d$-Ahlfor's regular metric space (which includes any $d$-manifold like the $d$-cube $[0,1]^d$ in the case $d$ is an integer but also fractals of dimension $d$ when $d$ is real-valued), our results imply that the greedy and nearest-neighbor heuristics have emph{additive} errors from optimal on the order of the emph{optimal} tour length through emph{random} points in the same space, for $d>1$." @default.
- W4387432217 created "2023-10-09" @default.
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- W4387432217 date "2023-10-04" @default.
- W4387432217 modified "2023-10-09" @default.
- W4387432217 title "The bright side of simple heuristics for the TSP" @default.
- W4387432217 doi "https://doi.org/10.48550/arxiv.2310.03222" @default.
- W4387432217 hasPublicationYear "2023" @default.
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