Add FrozenGraph (without tests)

README.md

@@ -6,7 +6,7 @@ This crate provides data structures to model graphs and to perform algorithms on
 
 Currently supported are:
 
-* Undirected graph types `Graph` and `AppendGraph`, built on a flat, index-based adjacency list,
+* Undirected graph types `Graph`, `AppendGraph`, and `FrozenGraph`, built on a flat, index-based adjacency list,
 * Maps to freely associate custom data with vertices and edges, 
 * Connectivity and pathing algorithms: Dijkstra's algorithm, DFS, and BFS in different variants,
 * Exposed traits to implement custom graph data structures or algorithms.

src/lib.rs

@@ -5,8 +5,8 @@
 //!
 //! Currently supported are:
 //!
-//! * Undirected graph types [`Graph`] and [`AppendGraph`] built on a flat, index-based adjacency
+//! * Undirected graph types [`Graph`], [`AppendGraph`], and [`FrozenGraph`] built on a flat,
-//! list,
+//! index-based adjacency list,
 //! * [`ElementMap`] to freely associate custom data with vertices and edges,
 //! * Connectivity and pathing algorithms: [Dijkstra's algorithm], [DFS], and [BFS] in different
 //! variants,
@@ -62,9 +62,11 @@
 //!
 //! # Graph types
 //!
-//! [`Graph`] and [`AppendGraph`] both implement [`GraphTopology`] using a flat, index-based adjacency
+//! [`Graph`], [`AppendGraph`], and [`FrozenGraph`] all implement [`GraphTopology`] using a flat,
-//! list to store edges, which means that vertex and edge insertions happen in `O(1)`. Degree
+//! index-based adjacency list to store edges. Degree lookups run in `O(1)`.
-//! lookups are also `O(1)`.
+//!
+//! [`Graph`] and [`AppendGraph`] implement [`GraphTopologyAddition`], which provides functionality
+//! for iterative graph construction. Vertex and edge insertions happen in `O(1)`.
 //!
 //! [`Graph`] additionally implements [`GraphTopologyDeletion`], thereby supporting deletion of
 //! vertices and edges.
@@ -73,6 +75,10 @@
 //! be smaller and more performant compared to [`Graph`] by not requiring the per-element generation
 //! tracking needed for stable handles after deletion.
 //!
+//! [`FrozenGraph`] uses a memory layout that is more cache-friendly for traversals than
+//! [`AppendGraph`], but the trade-off is that its topology must be constructed during its
+//! initialization. It cannot be modified afterward.
+//!
 //! # Vertices and edges
 //!
 //! Graphs in this library use stable indices [`GraphTopology::Vertex`] and [`GraphTopology::Edge`]
@@ -119,6 +125,7 @@
 //! [DFS]: crate::algorithms::dfs
 //! [`ElementMap`]: crate::maps::ElementMap
 //! [`AppendGraph`]: crate::models::AppendGraph
+//! [`FrozenGraph`]: crate::models::FrozenGraph
 //! [`Graph`]: crate::models::Graph
 //! [`traits`]: crate::traits
 //! [`GraphTopology`]: crate::traits::GraphTopology

src/models.rs

@@ -1,11 +1,13 @@
 //! Concrete graph topology models.
 
 pub mod append_graph;
+pub mod frozen_graph;
 pub mod graph;
 
-// TODO: Compressed-sparse-row graph model.
-
 pub use append_graph::{
     AppendGraph, AppendGraphEdgeMap, AppendGraphIncidence, AppendGraphVertexMap,
 };
+pub use frozen_graph::{
+    FrozenGraph, FrozenGraphEdgeMap, FrozenGraphIncidence, FrozenGraphVertexMap,
+};
 pub use graph::{Graph, GraphEdgeMap, GraphIncidence, GraphVertexMap};

src/models/append_graph.rs

@@ -67,7 +67,8 @@ impl IncidenceCursor<AppendGraph> for AppendGraphIncidenceCursor {
 ///
 /// `AppendGraph` is optimised for workloads that incrementally build a graph and query it
 /// repeatedly. [`Vertex`] and [`Edge`] handles are never invalidated. Use [`Graph`] instead if you
-/// need to remove vertices or edges.
+/// need to remove vertices or edges. Use [`FrozenGraph`] if you do not need incremental
+/// construction.
 ///
 /// Incidences are stored as interleaved adjacency lists in a single flat [`Vec`]. In general,
 /// vertex neighborhood traversals result in scattered index jumps.
@@ -93,6 +94,7 @@ impl IncidenceCursor<AppendGraph> for AppendGraphIncidenceCursor {
 /// [`add_vertex`]: Self::add_vertex
 /// [`add_edge`]: Self::add_edge
 /// [`degree`]: Self::degree
+/// [`FrozenGraph`]: crate::models::FrozenGraph
 /// [`Graph`]: crate::models::Graph
 pub struct AppendGraph {
     vertices: Vec<VertexIncidenceHeader>,

src/models/frozen_graph.rs

@@ -0,0 +1,250 @@
+//! [`FrozenGraph`], an undirected graph topology supporting only one-time construction.
+
+use std::ops::IndexMut;
+
+use crate::maps::ElementMap;
+use crate::traits::{GraphTopology, Incidence, IncidenceCursor};
+
+/// An opaque handle identifying a vertex in a [`FrozenGraph`].
+///
+/// Handles are stable for the lifetime of the graph. Obtain via graph methods like
+/// [`FrozenGraph::vertices`].
+#[derive(Copy, Clone, PartialEq, Eq, Debug, Hash)]
+pub struct Vertex(usize);
+
+/// An opaque handle identifying an edge in a [`FrozenGraph`].
+///
+/// Handles are stable for the lifetime of the graph. Obtain via graph methods like
+/// [`FrozenGraph::edges`].
+#[derive(Copy, Clone, PartialEq, Eq, Debug, Hash)]
+pub struct Edge(usize);
+
+/// An [`ElementMap`] for [`FrozenGraph`] vertices.
+pub type FrozenGraphVertexMap<T> = ElementMap<Vertex, T>;
+
+/// An [`ElementMap`] for [`FrozenGraph`] edges.
+pub type FrozenGraphEdgeMap<T> = ElementMap<Edge, T>;
+
+/// An [`Incidence`] for [`FrozenGraph`].
+pub type FrozenGraphIncidence = Incidence<Vertex, Edge>;
+
+#[derive(Copy, Clone)]
+struct IncidenceEntry {
+    adjacent: Vertex,
+    opposite: usize,
+}
+
+/// A resumable cursor over the incidences of a single vertex in a [`FrozenGraph`].
+///
+/// Obtain via [`FrozenGraph::incidence_cursor`]. See [`IncidenceCursor`] on usage guidance.
+#[derive(Copy, Clone)]
+pub struct FrozenGraphIncidenceCursor {
+    current: usize,
+    end: usize,
+}
+
+impl IncidenceCursor<FrozenGraph> for FrozenGraphIncidenceCursor {
+    fn next(&mut self, graph: &FrozenGraph) -> Option<FrozenGraphIncidence> {
+        if self.current < self.end {
+            let incidence = graph.normalize_incidence(self.current);
+            self.current += 1;
+            Some(incidence)
+        } else {
+            None
+        }
+    }
+}
+
+/// An undirected graph that supports only one-time construction, and no further modification.
+///
+/// `FrozenGraph` is optimised for workloads that repeatedly query a graph, but do not require
+/// changing it once it is constructed. [`Vertex`] and [`Edge`] handles are never invalidated. Use
+/// [`AppendGraph`] instead if you need to incrementally add vertices or edges, or [`Graph`] if you
+/// need to remove vertices or edges after initial construction.
+///
+/// `FrozenGraph` uses a compressed-sparse data representation. Incidences are stored as contiguous
+/// adjacency lists per vertex in a single flat [`Vec`]. Vertex neighborhood traversals are
+/// therefore cache-friendly without index jumps.
+///
+/// # Examples
+///
+/// ```
+/// use grapherity::prelude::*;
+/// use grapherity::models::{FrozenGraph, AppendGraph};
+///
+/// // Constructs a FrozenGraph instance via AppendGraph.
+/// let mut graph = AppendGraph::new();
+/// let v1 = graph.add_vertex();
+/// let v2 = graph.add_vertex();
+/// let e = graph.add_edge(v1, v2);
+/// let (graph, vertices, edges) = FrozenGraph::from_graph(&graph);
+///
+/// // Queries the FrozenGraph instance.
+/// assert!(graph.are_adjacent(vertices[v1], vertices[v2]));
+/// ```
+///
+/// # Time and space complexity
+///
+/// [`degree`] runs in *O(1)* time. Space complexity is *O(|V| + |E|)*.
+///
+/// [`degree`]: Self::degree
+/// [`AppendGraph`]: crate::models::AppendGraph
+/// [`Graph`]: crate::models::Graph
+pub struct FrozenGraph {
+    vertices: Vec<usize>,
+    incidences: Vec<IncidenceEntry>,
+}
+
+impl FrozenGraph {
+    /// Creates a graph instance as a copy of another graph.
+    ///
+    /// Returns the copied graph instance and two mappings of the `source` graph vertices and edges
+    /// to the new ones. Note that the returned mappings cannot support additional growth, i.e. any
+    /// vertex or edge added to the `source` graph after calling `from_graph` will map to an invalid
+    /// vertex or edge in the new `FrozenGraph`.
+    pub fn from_graph<G: GraphTopology>(
+        source: &G,
+    ) -> (
+        Self,
+        ElementMap<G::Vertex, Vertex>,
+        ElementMap<G::Edge, Edge>,
+    ) {
+        // Builds vertex list with sentinel and vertex map.
+        let mut vertex_map = source.vertex_map(Vertex(usize::MAX));
+        let mut vertices = Vec::with_capacity(source.vertex_count() + 1);
+        let mut offset = 0;
+        for (i, v) in source.vertices().enumerate() {
+            vertex_map[v] = Vertex(i);
+            vertices.push(offset);
+            offset += source.degree(v);
+        }
+        vertices.push(offset);
+
+        // Builds incidence list and edge map. Uses "usize::MAX" as "unset" here: an edge can never
+        // be normalized to "usize::MAX", since it must be the smaller index of two incidences.
+        const UNSET: usize = usize::MAX;
+        let mut edge_map = source.edge_map(Edge(UNSET));
+        let mut incidences = Vec::with_capacity(source.edge_count() * 2);
+        for v in source.vertices() {
+            for Incidence { vertex: u, edge: e } in source.incidences(v) {
+                let em = edge_map.index_mut(e);
+                if em.0 == UNSET {
+                    // Adds the first incidence for the edge, but we don't know the opposite, yet.
+                    *em = Edge(incidences.len());
+                    incidences.push(IncidenceEntry {
+                        adjacent: vertex_map[u],
+                        opposite: 0,
+                    });
+                } else {
+                    // Adds the second incidence for the edge and fills the opposite for the first.
+                    incidences[em.0].opposite = incidences.len();
+                    incidences.push(IncidenceEntry {
+                        adjacent: vertex_map[u],
+                        opposite: em.0,
+                    });
+                }
+            }
+        }
+
+        (
+            Self {
+                vertices,
+                incidences,
+            },
+            vertex_map,
+            edge_map,
+        )
+    }
+
+    fn raw_incidences(&self, v: Vertex) -> impl Iterator<Item = usize> {
+        self.vertices[v.0]..self.vertices[v.0 + 1]
+    }
+
+    fn normalize_edge(&self, e: usize) -> Edge {
+        let f = self.incidences[e].opposite;
+        Edge(if e < f { e } else { f })
+    }
+
+    fn normalize_incidence(&self, i: usize) -> FrozenGraphIncidence {
+        let entry = &self.incidences[i];
+        Incidence {
+            vertex: entry.adjacent,
+            edge: Edge(if i < entry.opposite {
+                i
+            } else {
+                entry.opposite
+            }),
+        }
+    }
+}
+
+impl<G: GraphTopology> From<&G> for FrozenGraph {
+    fn from(graph: &G) -> Self {
+        Self::from_graph(graph).0
+    }
+}
+
+impl GraphTopology for FrozenGraph {
+    type Vertex = Vertex;
+    type Edge = Edge;
+    type IncidenceCursor = FrozenGraphIncidenceCursor;
+
+    fn vertex_count(&self) -> usize {
+        self.vertices.len() - 1
+    }
+
+    fn vertex_map<T: Clone>(&self, default: T) -> ElementMap<Self::Vertex, T> {
+        ElementMap::new(default, |v| v.0, self.vertex_count())
+    }
+
+    fn edge_count(&self) -> usize {
+        self.incidences.len() / 2
+    }
+
+    fn edge_map<T: Clone>(&self, default: T) -> ElementMap<Self::Edge, T> {
+        ElementMap::new(default, |e| e.0, self.edge_count())
+    }
+
+    fn degree(&self, v: Self::Vertex) -> usize {
+        self.vertices[v.0 + 1] - self.vertices[v.0]
+    }
+
+    fn are_adjacent(&self, v1: Self::Vertex, v2: Self::Vertex) -> bool {
+        self.adjacent_vertices(v1).any(|x| x == v2)
+    }
+
+    fn vertices(&self) -> impl Iterator<Item = Self::Vertex> {
+        (0..self.vertices.len() - 1).map(Vertex)
+    }
+
+    fn adjacent_vertices(&self, v: Self::Vertex) -> impl Iterator<Item = Self::Vertex> {
+        self.raw_incidences(v).map(|i| self.incidences[i].adjacent)
+    }
+
+    fn incident_vertices(&self, e: Self::Edge) -> (Self::Vertex, Self::Vertex) {
+        let entry = &self.incidences[e.0];
+        (self.incidences[entry.opposite].adjacent, entry.adjacent)
+    }
+
+    fn edges(&self) -> impl Iterator<Item = Self::Edge> {
+        self.incidences
+            .iter()
+            .enumerate()
+            .filter_map(|(i, x)| (i < x.opposite).then_some(Edge(i)))
+    }
+
+    fn incident_edges(&self, v: Self::Vertex) -> impl Iterator<Item = Self::Edge> {
+        self.raw_incidences(v).map(|i| self.normalize_edge(i))
+    }
+
+    fn incidences(&self, v: Self::Vertex) -> impl Iterator<Item = FrozenGraphIncidence> {
+        self.raw_incidences(v).map(|i| self.normalize_incidence(i))
+    }
+
+    fn incidence_cursor(&self, v: Self::Vertex) -> Self::IncidenceCursor {
+        FrozenGraphIncidenceCursor {
+            current: self.vertices[v.0],
+            end: self.vertices[v.0 + 1],
+        }
+    }
+}