Before revision:  Example applications include the first constant-factor approximation algorithms whose running-time is polynomial in n for the following fundamental problems: (i) Constrained \ell_z Linear Regression: Given z>0, n vectors p_1,\cdots,p_n on the plane, and a vector b\in\mathbb{R^n, compute a unit vector x and a permutation \pi:
After revision:  Example applications include the first constant-factor approximation algorithms whose running-time is polynomial in n for the fundamental problem of p_1,\cdots,p_n on the plane, and a vector b\in\mathbb{R^n, compute a unit vector x and a permutation \pi: