Bird rule for minimum cost spanning tree problems
Given a graph with at least one minimum cost spanning tree,
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.
- vector containing the nodes of the graph, identified by a number that goes from $1$ to the order of the graph.
- 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.
mstBirdreturns a matrix with the agents and their costs.
The more general function mstRules.
# 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)