Outcomes of voting and planning in single facility location problems (Q1060128)

Consider the problem of finding a single facility on a network on which a given number of users are located. If a voting procedure is used, the optimal solution is a point, called a Condorcet point, such that no other is closer to an absolute majority of users. If a planning procedure is used, the optimal solution is a median which minimizes the sum of all distances to the users. The author first shows that the solutions of the two procedures coincide if the given network is a cactus. Then a polynomial algorithm is given to find the set of Condorcet points for a cactus. Finally, the outcomes of the two procedures are compared in terms of the cyclic structure and the number of users in the network.