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- W2950365512 abstract "This paper presents a polynomial-time $1/2$-approximation algorithm for maximizing nonnegative $k$-submodular functions. This improves upon the previous $max{1/3, 1/(1+a)}$-approximation by Ward and v{Z}ivn'y~(SODA'14), where $a=max{1, sqrt{(k-1)/4}}$. We also show that for monotone $k$-submodular functions there is a polynomial-time $k/(2k-1)$-approximation algorithm while for any $varepsilon>0$ a $((k+1)/2k+varepsilon)$-approximation algorithm for maximizing monotone $k$-submodular functions would require exponentially many queries. In particular, our hardness result implies that our algorithms are asymptotically tight. We also extend the approach to provide constant factor approximation algorithms for maximizing skew-bisubmodular functions, which were recently introduced as generalizations of bisubmodular functions." @default.
- W2950365512 created "2019-06-27" @default.
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- W2950365512 date "2015-12-21" @default.
- W2950365512 modified "2023-09-30" @default.
- W2950365512 title "Improved Approximation Algorithms for <i>k</i>-Submodular Function Maximization" @default.
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- W2950365512 doi "https://doi.org/10.1137/1.9781611974331.ch30" @default.
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