The Wikipedia article on Ring signatures states that
CryptoNote implements O(n) ring signature scheme by Fujisaki and Suzuki in p2p payments to achieve sender's untraceability.
More efficient algorithms have appeared recently. There are schemes with the sublinear size of the signature, as well as with constant size.
Would these more efficient algorithms be usable for Monero (through a hard-fork) to reduce or even avoid the increase in size of high-mixin transactions?
 Fujisaki, Eiichiro (2011). "Sub-linear size traceable ring signatures without random oracles".
 Au, Man Ho; Liu, Joseph K.; Susilo, Willy; Yuen, Tsz Hon (2006). "Constant-Size ID-Based Linkable and Revocable-iff-Linked Ring Signature".