cooptrees (version 1.0)

maERO: ERO rule for minimum cost arborescence problems

Description

Given a graph with a minimum cost arborescence, the maERO function divides the cost of the arborescence among the agents according to the ERO rule. For that purpose, the irreducible form of the problem is obtained. The ERO rule is just the Shapley value of the cooperative game associated with the irreducible form.

Usage

maERO(nodes, arcs)

Arguments

nodes

vector containing the nodes of the graph, identified by a number that goes from $1$ to the order of the graph.

arcs

matrix with the list of arcs of the graph. Each row represents one arc. The first two columns contain the two endpoints of each arc and the third column contains their weights.

Value

maERO returns a matrix with the agents and their costs.

See Also

The more general function maRules.

Examples

# Graphs
nodes <- 1:4
arcs <- matrix(c(1,2,7, 1,3,6, 1,4,4, 2,3,8, 2,4,6, 3,2,6,
                 3,4,5, 4,2,5, 4,3,7), ncol = 3, byrow = TRUE)
# ERO
maERO(nodes, arcs)