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### Open Access Journals

JIMO

In this paper, we consider the $2$-catalog segmentation problem. For
the disjoint version, we propose an approximation
algorithm based on the non-uniform rotation technique using a
semidefinite programming ($SDP$) relaxation. We give the
performance curve depending on the ratio between the value of optimal
SDP solution and the total weight. In this curve, the
lowest point implies the approximation ratio is $0.7317$ which is the best ratio for the disjoint version until now.
We also consider the performance curve of the joint version.

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