Hard Metrics from Cayley Graphs of Abelian Groups
نویسندگان
چکیده
Hard metrics are the class of extremal metrics with respect to embedding into Euclidean spaces: they incur Ω(logn) multiplicative distortion, which is as large as it can possibly get for any metric space of size n. Besides being very interesting objects akin to expanders and good error-correcting codes, and having a rich structure, such metrics are important for obtaining lower bounds in combinatorial optimization, e. g., on the value of MinCut/MaxFlow ratio for multicommodity flows. For more than a decade, a single family of hard metrics was known (see London et al. (Combinatorica 1995) and Aumann and Rabani (SICOMP 1998)). Recently, a different family was found by Khot and Naor (FOCS 2005). In this paper we present a general method of constructing hard metrics. Our results extend to embeddings into negative type metric spaces and into `1. ACM Classification: F.2.2, G.2.2 AMS Classification: 11J83, 52C45, 05C25
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