From 96203daa3d30859deb77577cca6da9d4abb1ab1b Mon Sep 17 00:00:00 2001 From: Yu Cong Date: Fri, 23 May 2025 11:01:33 +0800 Subject: [PATCH] is there any embedding thm only bounding small number of vertices? --- main.pdf | Bin 121932 -> 122161 bytes main.tex | 1 + 2 files changed, 1 insertion(+) diff --git a/main.pdf b/main.pdf index 34d52ef5f650ee030e44eeecd425efc6ac69ad3e..94c3aa0c3ae1ed35d68433843633c9b6e68b5d0a 100644 GIT binary patch delta 12596 zcmaiaQ* zUYTrzsqcWPd({VLXHLHp0;2{s>ufl0aQ*Uo(LA*lRoB+j`w714m*M=2GC4ZAs#H#W zJo8T}`S5-S2|Jnj$ive{EWEf((WP_)BT0lTgjLS90Af^(gM``ReMsBM!rGXip;Es@ zN=Txa4cj|Q5iv2Y&R9fT3LJa9WYTGZm@AuZY)w$*-A&^Py4k zgbf)d-H+MQaR=2{>~#oFAJ$wMn|dkzjyG;6`^n~S3Bt0vS2n}2Qe3b_CY#nTC7H@a z4U1+!icr7bl^3q{qfvnOw^ABSg)W{pY6bPtitF0b-VKZ~CQP=!s3c^1u|)|o{8{t` zSOW$`W+bBGUS$r3!T1;;Ad;iq30v0vKN3=cc`X6wL}xZ*;_zz=@y9(3SX7#^_xYO! z3v2bZ(evL`Sygm7WH^L6ri1%RXmjcJ+m5mb@&tEO=uyw%eiT8gi7|D-$xawDn_M{r z%JXqL0KB{zg)ctqcX6J>oNRy8!s6HS!*dT79U;;jJ?!8`-UT-hy9v61lb%3U-p9zA 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b/main.tex index d13ce0b..4456585 100644 --- a/main.tex +++ b/main.tex @@ -192,6 +192,7 @@ I think the intuition behind this SDP relaxation is almost the same as \metric{} \end{enumerate} The Lasserre relaxation of SDP automatically satisfies 1 and 2. But I believe there may be some very strange kind of metric that embeds into $\ell_1$ well? +Another possible approach for \nonuscut{} would be making the number of demand vertices small and then applying a metric embedding (contraction) to $\ell_1$ with better distortion on those vertices. \bibliographystyle{alpha} \bibliography{ref} \end{document}