maBird: Bird rule for minimum cost arborescence problems

In cooptrees: Cooperative aspects of optimal trees in weighted graphs

Description

Given a graph with a minimum cost arborescence, the maBird function divides the cost of this arborescence among the agents. For that purpose it, uses the Bird rule, where each agent pays the cost of the last arc that connects him to the source.

Usage

maBird(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

maBird returns a matrix with the agents and their costs.

See Also

The more general function maRules.

Examples

# Graph
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)
# Bird
maBird(nodes, arcs)

Example output

Loading required package: igraph

Attaching package: 'igraph'

The following objects are masked from 'package:stats':

    decompose, spectrum

The following object is masked from 'package:base':

    union

Loading required package: optrees
     agent cost
[1,]     2    5
[2,]     3    6
[3,]     4    4

cooptrees documentation built on May 2, 2019, 3:59 p.m.