# mstBird

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##### Bird rule for minimum cost spanning tree problems

Given a graph with at least one minimum cost spanning tree, the mstBird function divides the cost of the tree obtained with Prim's algorithm among the agents. For that purpose it uses the Bird rule, where each agent pays the cost of the arc that connects him to the tree source.

##### Usage
mstBird(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

mstBird returns a matrix with the agents and their costs.

The more general function mstRules.

• mstBird
##### Examples
# Graphs
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)
# Bird
mstBird(nodes, arcs)

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

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