# mstRules

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##### Allocation rules for minimum cost spanning tree problem

Given a graph with at least one minimum cost spanning tree, the mstRules function divides the cost of the tree among the agents according to the most known rules: "Bird", "Dutta-Kar", "Kar", "ERO".

##### Usage
mstRules(nodes, arcs, rule, algorithm = "Kruskal", show.data = TRUE)
##### 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.
rule
denotes the chosen allocation rule: "Bird", "Dutta-Kar", "Kar" or "ERO".
algorithm
denotes the algorithm used with the ERO rule: "Kruskal".
show.data
logical value indicating if the function displays the console outputTRUE or no FALSE. The deafult is TRUE.
##### Value

mstRules returns a matrix with the agents and the cost that each one of them has to pay. It also prints the result in console.

• mstRules
##### Examples
# Graph
nodes <- 1:4
arcs <- matrix(c(1,2,6, 1,3,10, 1,4,6, 2,3,4, 2,4,6, 3,4,4),
byrow = TRUE, ncol = 3)
# Allocation Rules
mstRules(nodes, arcs, rule = "Bird")
mstRules(nodes, arcs, rule = "Dutta-Kar")
mstRules(nodes, arcs, rule = "Kar")
mstRules(nodes, arcs, rule = "ERO", algorithm = "Kruskal")

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

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