The dispersion problem is a variant of the facility location problem. Given a set P of n points and an integer k, we intend to find a subset S of P with |S|=k such that the cost min_p∈S{cost(p)} is maximized, where cost(p) is the sum of the distances from p to the nearest c points in S. We call the problem the dispersion problem with partial c sum cost, or the PcS-dispersion problem. In this paper we present two algorithms to solve the P2S-dispersion problem(c=2) if all points of P are on a line. The running times of the algorithms are O(kn² log n) and O(n log n), respectively. We also present an algorithm to solve the PcS-dispersion problem if all points of P are on a line. The running time of the algorithm is O(kn^c+1).