“…The following list of references on this problem demonstrates the level of interest in this problem in the field of operations research and statistics: Ayer et al (1955), Brunk (1955), Robertson and Waltman (1968), Gebhardt (1970), Barlow et al (1972), Robertson andWright (1973, 1980), Ubhaya (1974aUbhaya ( , 1974bUbhaya ( , 1979Ubhaya ( , 1987, Casady and Cryer (1976), Goldstein and Kruskal (1976), Dykstra (1981), Lee (1983), Maxwell and Muchstadt (1983), Roundy (1986), Menendez and Salvador (1987), Robertson et al (1988), Chakravarti (1989), Best and Chakravarti (1990), Stromberg (1991), Best and Tan (1993), Tamir (1993), Eddy et al (1995), Pardalos et al (1995), Shi (1995), Best et al (2000), Liu and Ubhaya (1997), Schell and Singh (1997), and Pardalos and Xue (1999). It is well known that the isotone regression problem for p = 1 can be solved in O n log n time, and for p = 2 and p = , it can be solved in O n time (see, for example, Best and Chakravarti 1990, Pardalos et al 1995, and Liu and Ubhaya 1997.…”