ERO rule for minimum cost arborescence problems
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.
- vector containing the nodes of the graph, identified by a number that goes from $1$ to the order of the graph.
- 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.
maEROreturns a matrix with the agents and their costs.
The more general function maRules.
# 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)