Finding the Jaccard median

Authors:
Flavio Chierichetti;Ravi Kumar;Sandeep Pandey;Sergei Vassilvitskii
Affiliations:
Sapienza University of Rome, Italy;Yahoo! Research, Sunnyvale, CA;Yahoo! Research, Sunnyvale, CA;Yahoo! Research, Sunnyvale, CA
Venue:
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Year:
2010

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Abstract

The median problem in the weighted Jaccard metric was analyzed by Späth in 1981. Up until now, only an exponential-time exact algorithm was known. We (a) obtain a PTAS for the weighted Jaccard median problem and (b) show that the problem does not admit a FPTAS (assuming P ≠ NP), even when restricted to binary vectors. The PTAS is built on a number of different algorithmic ideas and the hardness result makes use of an especially interesting gadget.