Efficient algorithms for subdominant cycle-complete cost functions and cycle-complete solutions

The cycle-complete solution introduced by Trudeau (2012) is a solution concept for minimum cost spanning tree games and was proved to have desirable properties such as core-selection and sensitivity to change of the cost function. The cycle-complete solution is defined as the Shapley value of the minimum cost spanning tree game associated with the subdominant cycle-complete cost function of a given cost function. In this study, we characterize subdominant cycle-complete cost functions and provide an O(n2logn) time algorithm for computing such functions, where n is the number of players. This algorithm leads to a new algorithm for computing the cycle-complete solution of a minimum cost spanning tree game with an O(n2logn) time bound.