feat: feedback_vertex_set() finds a minimum feedback vertex set in …

…a graph
igraph · Oct 22, 2024 · 9896898 · 9896898
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commit 9896898
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diff --git a/NAMESPACE b/NAMESPACE
@@ -348,6 +348,7 @@ export(farthest.nodes)
 export(farthest_vertices)
 export(fastgreedy.community)
 export(feedback_arc_set)
+export(feedback_vertex_set)
 export(fit_hrg)
 export(fit_power_law)
 export(forest.fire.game)

diff --git a/R/aaa-auto.R b/R/aaa-auto.R
@@ -1231,6 +1231,28 @@ feedback_arc_set_impl <- function(graph, weights=NULL, algo=c("approx_eades", "e
   res
 }
 
+feedback_vertex_set_impl <- function(graph, weights=NULL, algo=c("exact_ip")) {
+  # Argument checks
+  ensure_igraph(graph)
+  if (is.null(weights) && "weight" %in% vertex_attr_names(graph)) {
+    weights <- V(graph)$weight
+  }
+  if (!is.null(weights) && any(!is.na(weights))) {
+    weights <- as.numeric(weights)
+  } else {
+    weights <- NULL
+  }
+  algo <- switch(igraph.match.arg(algo), "exact_ip"=0L)
+
+  on.exit( .Call(R_igraph_finalizer) )
+  # Function call
+  res <- .Call(R_igraph_feedback_vertex_set, graph, weights, algo)
+  if (igraph_opt("return.vs.es")) {
+    res <- create_vs(graph, res)
+  }
+  res
+}
+
 is_loop_impl <- function(graph, eids=E(graph)) {
   # Argument checks
   ensure_igraph(graph)

diff --git a/R/structural.properties.R b/R/structural.properties.R
@@ -1878,6 +1878,36 @@ topo_sort <- function(graph, mode = c("out", "all", "in")) {
 #' @cdocs igraph_feedback_arc_set
 feedback_arc_set <- feedback_arc_set_impl
 
+#' Finding a feedback vertex set in a graph
+#'
+#' @description 
+#' `r lifecycle::badge("experimental")`
+#'
+#' A feedback vertex set of a graph is a subset of vertices whose removal breaks
+#' all cycles in the graph. Finding a _minimum_ feedback vertex set is an
+#' NP-complete problem, both on directed and undirected graphs.
+#'
+#' @param graph The input graph
+#' @param weights Potential vertex weights. If the graph has a vertex
+#'   attribute called \sQuote{`weight`}, and this argument is
+#'   `NULL`, then the vertex attribute is used automatically. The goal of
+#'   the feedback vertex set problem is to find a feedback vertex set with
+#'   the smallest total weight.
+#' @param algo Specifies the algorithm to use. Currently, \dQuote{`exact_ip`},
+#'   which solves the feedback vertex set problem with an exact integer
+#'   programming approach, is the only option.
+#' @return A vertex sequence (by default, but see the `return.vs.es` option
+#'   of [igraph_options()]) containing the feedback vertex set.
+#' @keywords graphs
+#' @family structural.properties
+#' @family cycles
+#' @export
+#' @examples
+#'
+#' g <- make_lattice(c(3,3))
+#' feedback_vertex_set(g)
+feedback_vertex_set <- feedback_vertex_set_impl
+
 #' Girth of a graph
 #'
 #' The girth of a graph is the length of the shortest circle in it.

diff --git a/man/bfs.Rd b/man/bfs.Rd
diff --git a/man/components.Rd b/man/components.Rd
diff --git a/man/constraint.Rd b/man/constraint.Rd
diff --git a/man/coreness.Rd b/man/coreness.Rd
diff --git a/man/degree.Rd b/man/degree.Rd
diff --git a/man/dfs.Rd b/man/dfs.Rd
diff --git a/man/distances.Rd b/man/distances.Rd
diff --git a/man/edge_density.Rd b/man/edge_density.Rd
diff --git a/man/ego.Rd b/man/ego.Rd
diff --git a/man/feedback_arc_set.Rd b/man/feedback_arc_set.Rd
diff --git a/man/feedback_vertex_set.Rd b/man/feedback_vertex_set.Rd
diff --git a/man/girth.Rd b/man/girth.Rd
diff --git a/man/has_eulerian_path.Rd b/man/has_eulerian_path.Rd
diff --git a/man/is_acyclic.Rd b/man/is_acyclic.Rd
diff --git a/man/is_dag.Rd b/man/is_dag.Rd
diff --git a/man/k_shortest_paths.Rd b/man/k_shortest_paths.Rd
diff --git a/man/knn.Rd b/man/knn.Rd
diff --git a/man/matching.Rd b/man/matching.Rd
diff --git a/man/reciprocity.Rd b/man/reciprocity.Rd
diff --git a/man/subcomponent.Rd b/man/subcomponent.Rd
diff --git a/man/subgraph.Rd b/man/subgraph.Rd
diff --git a/man/topo_sort.Rd b/man/topo_sort.Rd
diff --git a/man/transitivity.Rd b/man/transitivity.Rd
diff --git a/man/unfold_tree.Rd b/man/unfold_tree.Rd
diff --git a/man/which_multiple.Rd b/man/which_multiple.Rd
diff --git a/man/which_mutual.Rd b/man/which_mutual.Rd
diff --git a/src/cpp11.cpp b/src/cpp11.cpp
@@ -163,6 +163,7 @@ extern SEXP R_igraph_extended_chordal_ring(SEXP, SEXP, SEXP);
 extern SEXP R_igraph_famous(SEXP);
 extern SEXP R_igraph_farthest_points(SEXP, SEXP, SEXP, SEXP);
 extern SEXP R_igraph_feedback_arc_set(SEXP, SEXP, SEXP);
+extern SEXP R_igraph_feedback_vertex_set(SEXP, SEXP, SEXP);
 extern SEXP R_igraph_finalizer(void);
 extern SEXP R_igraph_find_cycle(SEXP, SEXP);
 extern SEXP R_igraph_forest_fire_game(SEXP, SEXP, SEXP, SEXP, SEXP);
@@ -616,6 +617,7 @@ static const R_CallMethodDef CallEntries[] = {
     {"R_igraph_famous",                                     (DL_FUNC) &R_igraph_famous,                                      1},
     {"R_igraph_farthest_points",                            (DL_FUNC) &R_igraph_farthest_points,                             4},
     {"R_igraph_feedback_arc_set",                           (DL_FUNC) &R_igraph_feedback_arc_set,                            3},
+    {"R_igraph_feedback_vertex_set",                        (DL_FUNC) &R_igraph_feedback_vertex_set,                         3},
     {"R_igraph_finalizer",                                  (DL_FUNC) &R_igraph_finalizer,                                   0},
     {"R_igraph_find_cycle",                                 (DL_FUNC) &R_igraph_find_cycle,                                  2},
     {"R_igraph_forest_fire_game",                           (DL_FUNC) &R_igraph_forest_fire_game,                            5},