Hard Metrics from Cayley Graphs of Abelian Groups

  • Ilan Newman
  • Yuri Rabinovich
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4393)


Hard metrics are the class of extremal metrics with respect to embedding into Euclidean Spaces: their distortion is as bad as it possibly gets, which is Ω(logn). Besides being very interesting objects akin to expanders and good codes, with rich structure of independent interest, 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 [10,3]). Recently, a different such family was found (see [8]), causing a certain excitement among the researchers in the area.

In this paper we present another construction of hard metrics, different from [10,3], and more general yet clearer and simpler than [8]. Our results naturally extend to NEG and to ℓ1.


Abelian Group Linear Code Cayley Graph Linear Distance Hard Metrics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Ilan Newman
    • 1
  • Yuri Rabinovich
    • 1
  1. 1.Computer Science Department, University of Haifa, Haifa 31905Israel

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