Dynamic Markov Chains ( dynamic_markov_chain )

Definition

A Markov Chain is a graph G in which each edge has an associated non-negative integer weight w[e]. For every node (with at least one outgoing edge) the total weight of the outgoing edges must be positive A random walk in a Markov chain starts at some node s and then performs steps according to the following rule:

Initially, s is the current node. Suppose node v is the current node and that e₀, ..., e_{d - 1} are the edges out of v. If v has no outgoing edge no further step can be taken. Otherwise, the walk follows edge e_iwith probability proportional to w[e_i] for all i, 0 < = i < d. The target node of the chosen edge becomes the new current node.

The include file is <LEDA/markov_chain.h>

#include < LEDA/markov_chain.h >

Creation

dynamic_markov_chain	M(graph G, edge_array<int> w, node s = nil)
		creates a Markov chain for the graph G with edge weights w. The node s is taken as the start vertex (G.first_node() if s is nil).

Operations

void	M.step(int T = 1)	performs T steps of the Markov chain.
node	M.current_node()	returns current vertex.
int	M.current_outdeg()	returns the outdegree of the current vertex.
int	M.number_of_steps()	returns number of steps performed.
int	M.number_of_visits(node v)
		returns number of visits to node v.
double	M.rel_freq_of_visit(node v)
		returns number of visits divided by the total number of steps.
int	M.set_weight(edge e, int g)
		changes the weight of edge e to g and returns the old weight of e