cooptrees (version 1.0)

mstKar: Kar rule for minimum cost spanning tree problems

Description

Given a graph with at least one minimum cost spanning tree, the mstKar function divides the cost of the tree among the agents according to the Kar rule. That rule is obtained with the Shapley value of the pessimistic game.

Usage

mstKar(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

mstKar returns a matrix with the agents and their costs.

See Also

The more general function 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)
# Kar
mstKar(nodes, arcs)