We present a $.73$-approximation algorithm for a disjoint $2$-Catalog Segmentation and $.63$-approximation algorithm for the joint version of the problem. Previously best known results are $.65$ and $.56$, respectively. The results are based on semidefinite programming and a subtle rounding method.
Citation
Working Paper, Department of Management Sciences, Henry, B. Tippie College of Business, The University of Iowa, Iowa City, IA, 52242, USA