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We consider the problem of minimizing ? j?NC j(x j), subject to the following chain constraints x 1 =x 2 = x 3 = 脗·脗·脗· = x n, where C j(x j) is a convex function of x j for each j ? N={1,2, ... ,n}. This problem is a generalization of theisotonic regression problems with complete order, an important class of problems in regression analysis that has been examined extensively in the literature. We refer to this problem as thegeneralized isotonic regression problem. In this paper, we focus on developing a fast-scaling algorithm to obtain an integer solution of the generalized isotonic regression problem. LetU denote the difference between an upper bound on an optimal value of x n and a lower bound on an optimal value of x 1. Under the assumption that the evaluation of any function C j (x j) takesO(1) time, we show that the generalized isotonic regression problem can be solved inO(n logU) time. This improves by a factor of n the previous best running time ofO(n 2 logU) to solve the same problem. In addition, when our algorithm is specialized to theisotonic median regression problem (where C j(x j)=c j|x j-a jI) for specified values ofc js anda js, the algorithm obtains a real-valued optimal solution inO(n logn) time. This time bound matches the best available time bound to solve the isotonic median regression problem, but our algorithm uses simpler data structures and may be easier to implement.