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//! The hypergraph used at every level of the hierarchy, stored in both
//! directions at once.
//!
//! Coarsening walks vertex -> hyperedges -> pins to find match candidates and
//! refinement walks hyperedge -> pins to update gains, so both incidence
//! directions are materialized rather than derived on demand. Only the finest
//! level has all-ones weights: coarsening sums what it merges.
use crate::Error;
/// A hypergraph with optional hyperedge weights.
#[derive(Clone, Debug, PartialEq, Eq)]
pub struct Hypergraph {
pub(super) num_vertices: usize,
/// Fine vertices collapsed into this one. Balance is measured in these
/// units and cut cost in hyperedge-weight units; the two are not
/// commensurate, which matters wherever a single quantity has to price both
/// (see `refine_flow`).
pub(super) vertex_weights: Vec<u32>,
/// Default: all 1s when no weights given.
pub(super) hyperedge_weights: Vec<u32>,
/// `pins[hyperedge_offsets[e]..hyperedge_offsets[e + 1]]` is hyperedge
/// `e`'s pin set.
pub(super) hyperedge_offsets: Vec<u32>,
pins: Vec<u32>,
/// `incident_hyperedges[vertex_hyperedge_offsets[v]..
/// vertex_hyperedge_offsets[v + 1]]` is vertex `v`'s incidence list.
pub(super) vertex_hyperedge_offsets: Vec<u32>,
incident_hyperedges: Vec<u32>,
}
impl Hypergraph {
/// Build a hypergraph over vertices `0..num_vertices`.
///
/// `hyperedge_weights`, when present, has one positive entry per
/// hyperedge. Pins
/// within each hyperedge must be unique. Singleton hyperedges are dropped;
/// repeated hyperedges are merged by adding their weights.
///
/// # Errors
///
/// Returns an error for empty, repeated, or out-of-range pins; a zero
/// weight; a weight count mismatch; or counts and total weight outside the
/// implementation's integer ranges.
pub fn new(
num_vertices: u32,
hyperedges: &[Vec<u32>],
hyperedge_weights: Option<&[u32]>,
) -> Result<Self, Error> {
let num_vertices = num_vertices as usize;
if hyperedges.len() > u32::MAX as usize {
return Err(Error::InvalidInput(format!(
"hyperedge count {} does not fit in u32",
hyperedges.len()
)));
}
let total_pins = hyperedges
.iter()
.try_fold(0usize, |total, pins| total.checked_add(pins.len()))
.ok_or_else(|| Error::InvalidInput("hypergraph pin count overflows usize".into()))?;
if total_pins > u32::MAX as usize {
return Err(Error::InvalidInput(format!(
"hypergraph pin count {total_pins} does not fit in u32"
)));
}
if let Some(hyperedge_weights) = hyperedge_weights
&& hyperedge_weights.len() != hyperedges.len()
{
return Err(Error::InvalidInput(format!(
"hypergraph has {} hyperedges but {} hyperedge weights",
hyperedges.len(),
hyperedge_weights.len()
)));
}
let mut normalized = Vec::with_capacity(hyperedges.len());
for (hyperedge, pins) in hyperedges.iter().enumerate() {
if pins.is_empty() {
return Err(Error::InvalidInput(format!(
"hyperedge {hyperedge} has no pins"
)));
}
let weight = hyperedge_weights.map_or(1, |weights| weights[hyperedge]);
if weight == 0 {
return Err(Error::InvalidInput(format!(
"hyperedge {hyperedge} has weight 0; weights must be positive"
)));
}
let mut pins = pins.clone();
pins.sort_unstable();
if let Some(&vertex) = pins.iter().find(|&&vertex| vertex as usize >= num_vertices) {
return Err(Error::InvalidInput(format!(
"hyperedge {hyperedge} contains vertex {vertex}, outside 0..{num_vertices}"
)));
}
if let Some(vertex) = pins
.windows(2)
.find(|pair| pair[0] == pair[1])
.map(|pair| pair[0])
{
return Err(Error::InvalidInput(format!(
"hyperedge {hyperedge} contains vertex {vertex} more than once"
)));
}
if pins.len() < 2 {
continue;
}
normalized.push((pins, weight));
}
normalized.sort_unstable_by(|left, right| left.0.cmp(&right.0));
let mut canonical_hyperedges: Vec<Vec<u32>> = Vec::with_capacity(normalized.len());
let mut canonical_weights: Vec<u32> = Vec::with_capacity(normalized.len());
for (pins, weight) in normalized {
if canonical_hyperedges
.last()
.is_some_and(|last| last.as_slice() == pins.as_slice())
{
let combined = canonical_weights
.last_mut()
.expect("a repeated hyperedge has a previous weight");
*combined = combined.checked_add(weight).ok_or_else(|| {
Error::InvalidInput("merged hyperedge weight does not fit in u32".into())
})?;
} else {
canonical_hyperedges.push(pins);
canonical_weights.push(weight);
}
}
let total_hyperedge_weight: u64 = canonical_weights
.iter()
.map(|&weight| u64::from(weight))
.sum();
if total_hyperedge_weight > u32::MAX as u64 {
return Err(Error::InvalidInput(format!(
"total hyperedge weight {total_hyperedge_weight} does not fit in u32"
)));
}
Ok(Self::from_hyperedges(
num_vertices,
&canonical_hyperedges,
Some(&canonical_weights),
))
}
/// Number of vertices in the hypergraph.
pub fn num_vertices(&self) -> u32 {
self.num_vertices as u32
}
/// Number of distinct non-singleton hyperedges after canonicalization.
pub fn num_hyperedges(&self) -> usize {
self.hyperedge_offsets.len() - 1
}
/// Canonical non-singleton hyperedges and their positive weights.
///
/// Pins within an edge are sorted. Equal input hyperedges appear once with
/// their weights added.
pub fn hyperedges(&self) -> impl ExactSizeIterator<Item = (&[u32], u32)> + '_ {
(0..self.num_hyperedges()).map(|hyperedge| {
(
self.hyperedge_pins_unmetered(hyperedge),
self.hyperedge_weights[hyperedge],
)
})
}
/// Pins are stored exactly as given: each hyperedge must already be
/// deduplicated, since `greedy_growing` and the FM passes compare a
/// running count of pins on one side against the hyperedge's pin count,
/// and a repeated pin makes a fully-contained hyperedge never reach its own
/// pin count. `weights` is parallel to `hyperedges`.
pub(super) fn from_hyperedges(
num_vertices: usize,
hyperedges: &[Vec<u32>],
weights: Option<&[u32]>,
) -> Self {
let mut hyperedge_offsets = Vec::with_capacity(hyperedges.len() + 1);
let mut pins = Vec::new();
hyperedge_offsets.push(0);
for hyperedge in hyperedges {
pins.extend_from_slice(hyperedge);
hyperedge_offsets.push(pins.len() as u32);
}
let hyperedge_weights = match weights {
Some(w) => w.to_vec(),
None => vec![1; hyperedges.len()],
};
let mut v_to_he: Vec<Vec<u32>> = vec![Vec::new(); num_vertices];
for (hei, he) in hyperedges.iter().enumerate() {
for &v in he {
v_to_he[v as usize].push(hei as u32);
}
}
let mut vertex_hyperedge_offsets = Vec::with_capacity(num_vertices + 1);
let mut incident_hyperedges = Vec::new();
vertex_hyperedge_offsets.push(0);
for list in &v_to_he {
incident_hyperedges.extend_from_slice(list);
vertex_hyperedge_offsets.push(incident_hyperedges.len() as u32);
}
Hypergraph {
num_vertices,
vertex_weights: vec![1; num_vertices],
hyperedge_weights,
hyperedge_offsets,
pins,
vertex_hyperedge_offsets,
incident_hyperedges,
}
}
/// One of the two ways into the pin structure, and therefore one of the two
/// places this family's work is charged.
///
/// Every coarsening, partitioning and refinement loop here reaches its data
/// through this accessor or through [`Hypergraph::vertex_hyperedges`], so
/// charging the length of the slice each hands back prices all of them from
/// one place rather than from a charge in every loop. A caller that takes a
/// slice only to read its length is charged for pins it never visits, which
/// is the safe direction for a clock whose job is to stop a build before a
/// wall does.
pub(super) fn charged_hyperedge_pins(&self, hei: usize) -> &[u32] {
let pins = self.hyperedge_pins_unmetered(hei);
crate::meter::charge(pins.len() as u64);
pins
}
fn hyperedge_pins_unmetered(&self, hei: usize) -> &[u32] {
let start = self.hyperedge_offsets[hei] as usize;
let end = self.hyperedge_offsets[hei + 1] as usize;
&self.pins[start..end]
}
/// How many pins each hyperedge has on each side of `part`.
///
/// The whole hypergraph gain model is a statement about these two numbers
/// reaching 0, 1 or 2, so every refiner starts by building them and then
/// maintains them across its own moves.
pub(super) fn pin_counts(&self, part: &[u8]) -> Vec<[u32; 2]> {
let mut counts = vec![[0u32; 2]; self.num_hyperedges()];
for (hei, he_counts) in counts.iter_mut().enumerate() {
for &v in self.charged_hyperedge_pins(hei) {
he_counts[part[v as usize] as usize] += 1;
}
}
counts
}
/// The other charged incidence direction.
pub(super) fn vertex_hyperedges(&self, v: usize) -> &[u32] {
let start = self.vertex_hyperedge_offsets[v] as usize;
let end = self.vertex_hyperedge_offsets[v + 1] as usize;
crate::meter::charge((end - start) as u64);
&self.incident_hyperedges[start..end]
}
}