Yuval Filmus, Yasushi Kawase, Yusuke Kobayashi and Yutaro Yamaguchi

Math of OR

We study the problem of maximizing *XOS functions*, which are functions that can be written as a maximum of linear functions. The number of linear functions is known as the *width*.

We show that the threshold inapproximability is $\Theta(n/\log n)$ in the general case, and $k-1$ for width $k$ XOS functions (where $k \geq 2$).

@article{FKKY2021,

title = {Tight Approximation for Unconstrained {XOS} Maximization},

author = {Yuval Filmus and Yasushi Kawase and Yusuke Kobayashi and Yutaro Yamaguchi},

journal = {Mathematics of Operations Research},

volume = {46},

number = {4},

year = {2021},

pages = {1599--1610}

}

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title = {Tight Approximation for Unconstrained {XOS} Maximization},

author = {Yuval Filmus and Yasushi Kawase and Yusuke Kobayashi and Yutaro Yamaguchi},

journal = {Mathematics of Operations Research},

volume = {46},

number = {4},

year = {2021},

pages = {1599--1610}

}