cooptrees (version 1.0)

mstDuttaKar: Dutta-Kar rule for minimum cost spanning tree problems

Description

Given a graph with at least one minimum cost spanning tree, the mstDuttaKar function divides the cost of the tree obtained with Prim's algorithm among the agents according to the Dutta-Kar rule. This rule specifies that each agent chooses to pay the minimum cost between the last arc that connects him to the source and the cost that rejects his successor. The order is set by Prim's algorithm.

Usage

mstDuttaKar(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

mstDuttaKar 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)
# Dutta-Kar
mstDuttaKar(nodes, arcs)