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arXiv · 1606.06421

Approximation of the weighted maximin dispersion problem over Lp-ball: SDP relaxation is misleading

Zuping Wu·Yong Xia·Shu Wang
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Abstract

Consider the problem of finding a point in a unit $n$-dimensional $\ell_p$-ball ($p\ge 2$) such that the minimum of the weighted Euclidean distance from given $m$ points is maximized. We show in this paper that the recent SDP-relaxation-based approximation algorithm [SIAM J. Optim. 23(4), 2264-2294, 2013] will not only provide the first theoretical approximation bound of $\frac{1-O\left(\sqrt{ \ln(m)/n}\right)}{2}$, but also perform much better in practice, if the SDP relaxation is removed and the optimal solution of the SDP relaxation is replaced by a simple scalar matrix.

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Zuping Wu, Yong Xia, Shu Wang. 2016-06-21. Approximation of the weighted maximin dispersion problem over Lp-ball: SDP relaxation is misleading. https://arxiv.org/abs/1606.06421

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