Add {all_pairs,single_source}_bellman_ford_path_length (#44)

* Add `{all_pairs,single_source}_bellman_ford_path_length`

That is, add these to `nxapi`:
- `all_pairs_bellman_ford_path_length`
- `single_source_bellman_ford_path_length`

* Implement `algorithms.bellman_ford_path_lengths` to compute in chunks

* Ignore diagonals during Bellman-Ford

* Add comment, and use `offdiag` more places.

* Do level BFS for Bellman-Ford when iso-valued (and non-negative)

* Use `"iso_value"` property more places instead of `A.ss.iso_value`

* Fail fast in these unlikely, but easily detected, cases

* Allow garbage collector to be enabled during benchmarks

* Automatically choose appropriate chunksize

* Use `nsplits="auto"` in square_clustering (default to 256 MB chunks)

Author: eriknw

.pre-commit-config.yaml

@@ -56,7 +56,7 @@ repos:
         # These versions need updated manually
         - flake8==6.0.0
         - flake8-comprehensions==3.10.1
-        - flake8-bugbear==23.1.20
+        - flake8-bugbear==23.2.13
         - flake8-simplify==0.19.3
   - repo: https://github.com/asottile/yesqa
     rev: v1.4.0

graphblas_algorithms/algorithms/centrality/katz.py

@@ -35,9 +35,9 @@ def katz_centrality(
             raise GraphBlasAlgorithmException("beta must have a value for every node")
 
     A = G._A
-    if A.ss.is_iso:
+    if (iso_value := G.get_property("iso_value")) is not None:
         # Fold iso-value into alpha
-        alpha *= A.ss.iso_value.get(1.0)
+        alpha *= iso_value.get(1.0)
         semiring = plus_first[float]
     else:
         semiring = plus_times[float]

graphblas_algorithms/algorithms/core.py

@@ -28,7 +28,7 @@ def k_truss(G: Graph, k) -> Graph:
             S = C
 
     # Remove isolate nodes
-    indices, _ = C.reduce_rowwise(monoid.any).to_coo()
+    indices, _ = C.reduce_rowwise(monoid.any).to_coo(values=False)
     Ktruss = C[indices, indices].new()
 
     # Convert back to networkx graph with correct node ids

graphblas_algorithms/algorithms/dag.py

@@ -9,7 +9,7 @@ def descendants(G, source):
     if source not in G._key_to_id:
         raise KeyError(f"The node {source} is not in the graph")
     index = G._key_to_id[source]
-    A = G._A
+    A = G.get_property("offdiag")
     q = Vector.from_coo(index, True, size=A.nrows, name="q")
     rv = q.dup(name="descendants")
     for _ in range(A.nrows):
@@ -25,7 +25,7 @@ def ancestors(G, source):
     if source not in G._key_to_id:
         raise KeyError(f"The node {source} is not in the graph")
     index = G._key_to_id[source]
-    A = G._A
+    A = G.get_property("offdiag")
     q = Vector.from_coo(index, True, size=A.nrows, name="q")
     rv = q.dup(name="descendants")
     for _ in range(A.nrows):

graphblas_algorithms/algorithms/exceptions.py

@@ -12,3 +12,7 @@ class EmptyGraphError(GraphBlasAlgorithmException):
 
 class PointlessConcept(GraphBlasAlgorithmException):
     pass
+
+
+class Unbounded(GraphBlasAlgorithmException):
+    pass

graphblas_algorithms/algorithms/link_analysis/pagerank_alg.py

@@ -49,11 +49,10 @@ def pagerank(
         row_degrees = G.get_property("plus_rowwise+")  # XXX: What about self-edges?
     S = (alpha / row_degrees).new(name="S")
 
-    if A.ss.is_iso:
+    if (iso_value := G.get_property("iso_value")) is not None:
         # Fold iso-value of A into S
         # This lets us use the plus_first semiring, which is faster
-        iso_value = A.ss.iso_value
-        if iso_value != 1:
+        if iso_value.get(1) != 1:
             S *= iso_value
         semiring = plus_first[float]
     else:

graphblas_algorithms/algorithms/shortest_paths/__init__.py

@@ -1,2 +1,3 @@
 from .dense import *
 from .generic import *
+from .weighted import *

graphblas_algorithms/algorithms/shortest_paths/generic.py

@@ -10,7 +10,7 @@ def has_path(G, source, target):
     dst = G._key_to_id[target]
     if src == dst:
         return True
-    A = G._A
+    A = G.get_property("offdiag")
     q_src = Vector.from_coo(src, True, size=A.nrows, name="q_src")
     seen_src = q_src.dup(name="seen_src")
     q_dst = Vector.from_coo(dst, True, size=A.nrows, name="q_dst")

graphblas_algorithms/algorithms/shortest_paths/weighted.py

@@ -0,0 +1,207 @@
+import numpy as np
+from graphblas import Matrix, Vector, binary, monoid, replace, select, unary
+from graphblas.semiring import any_pair, min_plus
+
+from ..exceptions import Unbounded
+
+__all__ = [
+    "single_source_bellman_ford_path_length",
+    "bellman_ford_path_lengths",
+]
+
+
+def single_source_bellman_ford_path_length(G, source):
+    # No need for `is_weighted=` keyword, b/c this is assumed to be weighted (I think)
+    index = G._key_to_id[source]
+    if G.get_property("is_iso"):
+        # If the edges are iso-valued (and positive), then we can simply do level BFS
+        is_negative, iso_value = G.get_properties("has_negative_edges+ iso_value")
+        if not is_negative:
+            d = _bfs_level(G, source, dtype=iso_value.dtype)
+            if iso_value != 1:
+                d *= iso_value
+            return d
+        # It's difficult to detect negative cycles with BFS
+        if G._A[index, index].get() is not None:
+            raise Unbounded("Negative cycle detected.")
+        if not G.is_directed() and G._A[index, :].nvals > 0:
+            # For undirected graphs, any negative edge is a cycle
+            raise Unbounded("Negative cycle detected.")
+
+    # Use `offdiag` instead of `A`, b/c self-loops don't contribute to the result,
+    # and negative self-loops are easy negative cycles to avoid.
+    # We check if we hit a self-loop negative cycle at the end.
+    A, has_negative_diagonal = G.get_properties("offdiag has_negative_diagonal")
+    if A.dtype == bool:
+        # Should we upcast e.g. INT8 to INT64 as well?
+        dtype = int
+    else:
+        dtype = A.dtype
+    n = A.nrows
+    d = Vector(dtype, n, name="single_source_bellman_ford_path_length")
+    d[index] = 0
+    cur = d.dup(name="cur")
+    mask = Vector(bool, n, name="mask")
+    one = unary.one[bool]
+    for _i in range(n - 1):
+        # This is a slightly modified Bellman-Ford algorithm.
+        # `cur` is the current frontier of values that improved in the previous iteration.
+        # This means that in this iteration we drop values from `cur` that are not better.
+        cur << min_plus(cur @ A)
+
+        # Mask is True where cur not in d or cur < d
+        mask << one(cur)
+        mask(binary.second) << binary.lt(cur & d)
+
+        # Drop values from `cur` that didn't improve
+        cur(mask.V, replace) << cur
+        if cur.nvals == 0:
+            break
+        # Update `d` with values that improved
+        d(cur.S) << cur
+    else:
+        # Check for negative cycle when for loop completes without breaking
+        cur << min_plus(cur @ A)
+        mask << binary.lt(cur & d)
+        if mask.reduce(monoid.lor):
+            raise Unbounded("Negative cycle detected.")
+    if has_negative_diagonal:
+        # We removed diagonal entries above, so check if we visited one with a negative weight
+        diag = G.get_property("diag")
+        cur << select.valuelt(diag, 0)
+        if any_pair(d @ cur):
+            raise Unbounded("Negative cycle detected.")
+    return d
+
+
+def bellman_ford_path_lengths(G, nodes=None, *, expand_output=False):
+    """
+
+    Parameters
+    ----------
+    expand_output : bool, default False
+        When False, the returned Matrix has one row per node in nodes.
+        When True, the returned Matrix has the same shape as the input Matrix.
+    """
+    # Same algorithms as in `single_source_bellman_ford_path_length`, but with
+    # `Cur` as a Matrix with each row corresponding to a source node.
+    if G.get_property("is_iso"):
+        is_negative, iso_value = G.get_properties("has_negative_edges+ iso_value")
+        if not is_negative:
+            D = _bfs_levels(G, nodes, dtype=iso_value.dtype)
+            if iso_value != 1:
+                D *= iso_value
+            if nodes is not None and expand_output and D.ncols != D.nrows:
+                ids = G.list_to_ids(nodes)
+                rv = Matrix(D.dtype, D.ncols, D.ncols, name=D.name)
+                rv[ids, :] = D
+                return rv
+            return D
+        if not G.is_directed():
+            # For undirected graphs, any negative edge is a cycle
+            if nodes is not None:
+                ids = G.list_to_ids(nodes)
+                if G._A[ids, :].nvals > 0:
+                    raise Unbounded("Negative cycle detected.")
+            elif G._A.nvals > 0:
+                raise Unbounded("Negative cycle detected.")
+
+    A, has_negative_diagonal = G.get_properties("offdiag has_negative_diagonal")
+    if A.dtype == bool:
+        dtype = int
+    else:
+        dtype = A.dtype
+    n = A.nrows
+    if nodes is None:
+        # TODO: `D = Vector.from_scalar(0, n, dtype).diag()`
+        D = Vector(dtype, n, name="bellman_ford_path_lengths_vector")
+        D << 0
+        D = D.diag(name="bellman_ford_path_lengths")
+    else:
+        ids = G.list_to_ids(nodes)
+        D = Matrix.from_coo(
+            np.arange(len(ids), dtype=np.uint64),
+            ids,
+            0,
+            dtype,
+            nrows=len(ids),
+            ncols=n,
+            name="bellman_ford_path_lengths",
+        )
+    Cur = D.dup(name="Cur")
+    Mask = Matrix(bool, D.nrows, D.ncols, name="Mask")
+    one = unary.one[bool]
+    for _i in range(n - 1):
+        Cur << min_plus(Cur @ A)
+        Mask << one(Cur)
+        Mask(binary.second) << binary.lt(Cur & D)
+        Cur(Mask.V, replace) << Cur
+        if Cur.nvals == 0:
+            break
+        D(Cur.S) << Cur
+    else:
+        Cur << min_plus(Cur @ A)
+        Mask << binary.lt(Cur & D)
+        if Mask.reduce_scalar(monoid.lor):
+            raise Unbounded("Negative cycle detected.")
+    if has_negative_diagonal:
+        diag = G.get_property("diag")
+        cur = select.valuelt(diag, 0)
+        if any_pair(D @ cur).nvals > 0:
+            raise Unbounded("Negative cycle detected.")
+    if nodes is not None and expand_output and D.ncols != D.nrows:
+        rv = Matrix(D.dtype, n, n, name=D.name)
+        rv[ids, :] = D
+        return rv
+    return D
+
+
+def _bfs_level(G, source, *, dtype=int):
+    if dtype == bool:
+        dtype = int
+    index = G._key_to_id[source]
+    A = G.get_property("offdiag")
+    n = A.nrows
+    v = Vector(dtype, n, name="bfs_level")
+    q = Vector(bool, n, name="q")
+    v[index] = 0
+    q[index] = True
+    any_pair_bool = any_pair[bool]
+    for i in range(1, n):
+        q(~v.S, replace) << any_pair_bool(q @ A)
+        if q.nvals == 0:
+            break
+        v(q.S) << i
+    return v
+
+
+def _bfs_levels(G, nodes=None, *, dtype=int):
+    if dtype == bool:
+        dtype = int
+    A = G.get_property("offdiag")
+    n = A.nrows
+    if nodes is None:
+        # TODO: `D = Vector.from_scalar(0, n, dtype).diag()`
+        D = Vector(dtype, n, name="bfs_levels_vector")
+        D << 0
+        D = D.diag(name="bfs_levels")
+    else:
+        ids = G.list_to_ids(nodes)
+        D = Matrix.from_coo(
+            np.arange(len(ids), dtype=np.uint64),
+            ids,
+            0,
+            dtype,
+            nrows=len(ids),
+            ncols=n,
+            name="bfs_levels",
+        )
+    Q = Matrix(bool, D.nrows, D.ncols, name="Q")
+    Q << unary.one[bool](D)
+    any_pair_bool = any_pair[bool]
+    for i in range(1, n):
+        Q(~D.S, replace) << any_pair_bool(Q @ A)
+        if Q.nvals == 0:
+            break
+        D(Q.S) << i
+    return D

graphblas_algorithms/algorithms/simple_paths.py

@@ -8,7 +8,7 @@ def is_simple_path(G, nodes):
         return False
     if len(nodes) == 1:
         return nodes[0] in G
-    A = G._A
+    A = G._A  # offdiag instead?
     if A.nvals < len(nodes) - 1:
         return False
     key_to_id = G._key_to_id