Improved lower bounds for embeddings into L1

Robert Krauthgamer*, Yuval Rabani

*Corresponding author for this work

Research output: Contribution to conferencePaperpeer-review

53 Scopus citations


We simplify and improve upon recent lower bounds on the minimum distortion of embedding certain finite metric spaces into LI. In particular, we show that for infinitely many values of n there are n-point metric spaces of negative type that require a distortion of Ω(log log n) for such an embedding, implying the same lower bound on the integrality gap of a well-known SDP relaxation for SPARSEST-CUT. This result builds upon and improves the recent lower bound of (log log n)1-6-o(1) due to Khot and Vishnoi [STOC 2005]. We also show that embedding the edit distance on {0, 1}n into L1 requires a distortion of Ω(log n). This result simplifies and improves a very recent lower bound due to Khot and Naor [FOCS 2005].

Original languageAmerican English
Number of pages8
StatePublished - 2006
Externally publishedYes
EventSeventeenth Annual ACM-SIAM Symposium on Discrete Algorithms - Miami, FL, United States
Duration: 22 Jan 200624 Jan 2006


ConferenceSeventeenth Annual ACM-SIAM Symposium on Discrete Algorithms
Country/TerritoryUnited States
CityMiami, FL


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