# maERO

From cooptrees v1.0
by Manuel Fontenla

##### 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.

##### 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)
```

*Documentation reproduced from package cooptrees, version 1.0, License: GPL-3*

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