A randomized strategyproof two-facility mechanism on Ptolemaic metric spaces achieves approximation ratio 11/3, and the best possible ratio is at least (1+√2)/2.
Non-positive curvature and the P tolemy inequality
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Breaking the 4-Approximation Barrier in Strategyproof Two-Facility Location
A randomized strategyproof two-facility mechanism on Ptolemaic metric spaces achieves approximation ratio 11/3, and the best possible ratio is at least (1+√2)/2.