A feedback arc set of a graph is a subset of edges whose removal breaks all cycles in the graph.
Usage
feedback_arc_set(graph, weights = NULL, algo = c("approx_eades", "exact_ip"))Arguments
- graph
The input graph
- weights
Potential edge weights. If the graph has an edge attribute called ‘
weight’, and this argument isNULL, then the edge attribute is used automatically. The goal of the feedback arc set problem is to find a feedback arc set with the smallest total weight.- algo
Specifies the algorithm to use. “
exact_ip” solves the feedback arc set problem with an exact integer programming algorithm that guarantees that the total weight of the removed edges is as small as possible. “approx_eades” uses a fast (linear-time) approximation algorithm from Eades, Lin and Smyth. “exact” is an alias to “exact_ip” while “approx” is an alias to “approx_eades”.
Value
An edge sequence (by default, but see the return.vs.es option
of igraph_options()) containing the feedback arc set.
Details
Feedback arc sets are typically used in directed graphs. The removal of a feedback arc set of a directed graph ensures that the remaining graph is a directed acyclic graph (DAG). For undirected graphs, the removal of a feedback arc set ensures that the remaining graph is a forest (i.e. every connected component is a tree).
References
Peter Eades, Xuemin Lin and W.F.Smyth: A fast and effective heuristic for the feedback arc set problem. Information Processing Letters 47:6, pp. 319-323, 1993
See also
Other structural.properties:
bfs(),
component_distribution(),
connect(),
constraint(),
coreness(),
degree(),
dfs(),
distance_table(),
edge_density(),
feedback_vertex_set(),
girth(),
is_acyclic(),
is_dag(),
is_matching(),
k_shortest_paths(),
knn(),
reciprocity(),
subcomponent(),
subgraph(),
topo_sort(),
transitivity(),
unfold_tree(),
which_multiple(),
which_mutual()
Graph cycles
feedback_vertex_set(),
find_cycle(),
girth(),
has_eulerian_path(),
is_acyclic(),
is_dag(),
simple_cycles()
Examples
g <- sample_gnm(20, 40, directed = TRUE)
feedback_arc_set(g)
#> + 5/40 edges from 9f62c9b:
#> [1] 9-> 8 15-> 9 15->10 16-> 3 16->12
feedback_arc_set(g, algo = "approx_eades")
#> + 5/40 edges from 9f62c9b:
#> [1] 9-> 8 15-> 9 15->10 16-> 3 16->12