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//! Submodule declaring `K_{2,3}` homeomorph detection for simple undirected
//! graphs.
//!
//! The current implementation follows Boyer's edge-addition outerplanarity
//! search structure for `K_{2,3}` detection. It treats `K_{2,3}` search as a
//! blocked-bicomp handler layered on the same DFS/pertinence/ext-face state
//! used by the outerplanarity engine.
use num_traits::AsPrimitive;
use super::topology_wrapper_macros::define_planarity_derived_error;
use crate::traits::{
UndirectedMonopartiteMonoplexGraph,
algorithms::{PlanarityError, planarity_detection},
};
define_planarity_derived_error!(
/// Error type for `K_{2,3}` homeomorph detection.
pub enum K23HomeomorphError => K23HomeomorphError,
mapper = map_planarity_error_to_k23_homeomorph_error,
self_loop = "The K23 homeomorph algorithm currently supports only simple undirected graphs and does not accept self-loops.",
parallel = "The K23 homeomorph algorithm currently supports only simple undirected graphs and does not accept parallel edges."
);
/// Trait providing `K_{2,3}` homeomorph detection for simple undirected graphs.
pub trait K23HomeomorphDetection: UndirectedMonopartiteMonoplexGraph {
/// Returns whether the graph contains a subgraph homeomorphic to `K_{2,3}`.
///
/// The implementation follows Boyer's outerplanarity-obstruction search:
/// it runs the outerplanarity walkdown, intercepts blocked bicomps, and
/// distinguishes `K_{2,3}` from separable `K_4` obstructions using the
/// same blocked-bicomp state.
///
/// # Errors
///
/// Returns an error when the graph violates the simple-undirected contract,
/// such as by containing self-loops, parallel edges, or malformed edge
/// endpoints from a custom graph implementation.
///
/// # Examples
///
/// ```rust
/// use geometric_traits::{
/// impls::{CSR2D, SortedVec, SymmetricCSR2D},
/// prelude::*,
/// traits::{EdgesBuilder, K23HomeomorphDetection, VocabularyBuilder},
/// };
///
/// fn build_undigraph(node_count: usize, edges: &[(usize, usize)]) -> UndiGraph<usize> {
/// let nodes: SortedVec<usize> = GenericVocabularyBuilder::default()
/// .expected_number_of_symbols(node_count)
/// .symbols((0..node_count).enumerate())
/// .build()
/// .unwrap();
///
/// let mut normalized_edges = edges.to_vec();
/// for (left, right) in &mut normalized_edges {
/// if *left > *right {
/// core::mem::swap(left, right);
/// }
/// }
/// normalized_edges.sort_unstable();
///
/// let matrix: SymmetricCSR2D<CSR2D<usize, usize, usize>> = UndiEdgesBuilder::default()
/// .expected_number_of_edges(normalized_edges.len())
/// .expected_shape(node_count)
/// .edges(normalized_edges.into_iter())
/// .build()
/// .unwrap();
///
/// UndiGraph::from((nodes, matrix))
/// }
///
/// let k23 = build_undigraph(5, &[(0, 2), (0, 3), (0, 4), (1, 2), (1, 3), (1, 4)]);
/// let k4 = build_undigraph(4, &[(0, 1), (0, 2), (0, 3), (1, 2), (1, 3), (2, 3)]);
///
/// assert!(k23.has_k23_homeomorph()?);
/// assert!(!k4.has_k23_homeomorph()?);
/// # Ok::<(), geometric_traits::errors::MonopartiteError<UndiGraph<usize>>>(())
/// ```
#[inline]
fn has_k23_homeomorph(&self) -> Result<bool, crate::errors::MonopartiteError<Self>>
where
Self: Sized,
Self::NodeId: AsPrimitive<usize>,
{
has_k23_homeomorph_simple_undirected_graph(self)
.map_err(map_planarity_error_to_k23_homeomorph_error::<Self>)
}
}
impl<G: ?Sized + UndirectedMonopartiteMonoplexGraph> K23HomeomorphDetection for G {}
pub(crate) fn has_k23_homeomorph_simple_undirected_graph<G>(
graph: &G,
) -> Result<bool, PlanarityError>
where
G: UndirectedMonopartiteMonoplexGraph,
G::NodeId: AsPrimitive<usize>,
{
planarity_detection::has_k23_homeomorph_simple_undirected_graph(graph)
}
#[cfg(test)]
mod tests {
use super::{K23HomeomorphError, map_planarity_error_to_k23_homeomorph_error};
use crate::{
errors::{
MonopartiteError, monopartite_graph_error::algorithms::MonopartiteAlgorithmError,
},
prelude::UndiGraph,
traits::algorithms::planarity_detection::{
preprocessing::LocalSimpleGraph, run_k23_homeomorph_engine,
},
};
#[test]
fn test_map_planarity_parallel_edge_error_to_k23_error() {
let error: MonopartiteError<UndiGraph<usize>> = map_planarity_error_to_k23_homeomorph_error(
crate::traits::algorithms::PlanarityError::ParallelEdgesUnsupported,
);
assert!(matches!(
error,
MonopartiteError::AlgorithmError(MonopartiteAlgorithmError::K23HomeomorphError(
K23HomeomorphError::ParallelEdgesUnsupported
))
));
}
#[test]
fn test_map_planarity_invalid_endpoint_error_to_k23_error() {
let error: MonopartiteError<UndiGraph<usize>> = map_planarity_error_to_k23_homeomorph_error(
crate::traits::algorithms::PlanarityError::InvalidEdgeEndpoint {
endpoint: 9,
node_count: 4,
},
);
assert!(matches!(
error,
MonopartiteError::AlgorithmError(MonopartiteAlgorithmError::K23HomeomorphError(
K23HomeomorphError::InvalidEdgeEndpoint { endpoint: 9, node_count: 4 }
))
));
}
#[test]
fn test_run_k23_engine_detects_three_path_theta() {
let graph =
LocalSimpleGraph::from_edges(5, &[[0, 2], [2, 1], [0, 3], [3, 1], [0, 4], [4, 1]])
.unwrap();
assert!(run_k23_homeomorph_engine(&graph.preprocess()));
}
#[test]
fn test_run_k23_engine_rejects_k4_pair() {
let graph =
LocalSimpleGraph::from_edges(4, &[[0, 1], [0, 2], [0, 3], [1, 2], [1, 3], [2, 3]])
.unwrap();
assert!(!run_k23_homeomorph_engine(&graph.preprocess()));
}
}