Add bellman_ford_path

README.md

@@ -178,6 +178,7 @@ dispatch pattern shown above.
 - Shortest Paths
   - all_pairs_bellman_ford_path_length
   - all_pairs_shortest_path_length
+  - bellman_ford_path
   - floyd_warshall
   - floyd_warshall_numpy
   - floyd_warshall_predecessor_and_distance

graphblas_algorithms/algorithms/_bfs.py

@@ -1,7 +1,7 @@
 """BFS routines used by other algorithms"""
 
 import numpy as np
-from graphblas import Matrix, Vector, binary, replace, unary
+from graphblas import Matrix, Vector, binary, indexunary, replace, semiring, unary
 from graphblas.semiring import any_pair
 
 
@@ -11,8 +11,13 @@ def _get_cutoff(n, cutoff):
     return cutoff + 1  # Inclusive
 
 
-def _plain_bfs(G, source, *, cutoff=None):
-    index = G._key_to_id[source]
+def _bfs_plain(G, source=None, target=None, *, index=None, cutoff=None):
+    if source is not None:
+        index = G._key_to_id[source]
+    if target is not None:
+        dst_id = G._key_to_id[target]
+    else:
+        dst_id = None
     A = G.get_property("offdiag")
     n = A.nrows
     v = Vector(bool, n, name="bfs_plain")
@@ -25,6 +30,8 @@ def _plain_bfs(G, source, *, cutoff=None):
         q(~v.S, replace) << any_pair_bool(q @ A)
         if q.nvals == 0:
             break
+        if dst_id is not None and dst_id in q:
+            break
         v(q.S) << True
     return v
 
@@ -83,8 +90,38 @@ def _bfs_levels(G, nodes, cutoff=None, *, dtype=int):
     return D
 
 
+def _bfs_parent(G, source, cutoff=None, *, target=None, transpose=False, dtype=int):
+    if dtype == bool:
+        dtype = int
+    index = G._key_to_id[source]
+    if target is not None:
+        dst_id = G._key_to_id[target]
+    else:
+        dst_id = None
+    A = G.get_property("offdiag")
+    if transpose and G.is_directed():
+        A = A.T  # TODO: should we use "AT" instead?
+    n = A.nrows
+    v = Vector(dtype, n, name="bfs_parent")
+    q = Vector(dtype, n, name="q")
+    v[index] = index
+    q[index] = index
+    min_first = semiring.min_first[v.dtype]
+    index = indexunary.index[v.dtype]
+    cutoff = _get_cutoff(n, cutoff)
+    for _i in range(1, cutoff):
+        q(~v.S, replace) << min_first(q @ A)
+        if q.nvals == 0:
+            break
+        v(q.S) << q
+        if dst_id is not None and dst_id in q:
+            break
+        q << index(q)
+    return v
+
+
 # TODO: benchmark this and the version commented out below
-def _plain_bfs_bidirectional(G, source):
+def _bfs_plain_bidirectional(G, source):
     # Bi-directional BFS w/o symmetrizing the adjacency matrix
     index = G._key_to_id[source]
     A = G.get_property("offdiag")
@@ -125,7 +162,7 @@ def _plain_bfs_bidirectional(G, source):
 
 
 """
-def _plain_bfs_bidirectional(G, source):
+def _bfs_plain_bidirectional(G, source):
     # Bi-directional BFS w/o symmetrizing the adjacency matrix
     index = G._key_to_id[source]
     A = G.get_property("offdiag")

graphblas_algorithms/algorithms/components/connected.py

@@ -1,12 +1,12 @@
-from .._bfs import _plain_bfs
+from .._bfs import _bfs_plain
 from ..exceptions import PointlessConcept
 
 
 def is_connected(G):
     if len(G) == 0:
         raise PointlessConcept("Connectivity is undefined for the null graph.")
-    return _plain_bfs(G, next(iter(G))).nvals == len(G)
+    return _bfs_plain(G, next(iter(G))).nvals == len(G)
 
 
 def node_connected_component(G, n):
-    return _plain_bfs(G, n)
+    return _bfs_plain(G, n)

graphblas_algorithms/algorithms/components/weakly_connected.py

@@ -1,8 +1,8 @@
-from .._bfs import _plain_bfs_bidirectional
+from .._bfs import _bfs_plain_bidirectional
 from ..exceptions import PointlessConcept
 
 
 def is_weakly_connected(G):
     if len(G) == 0:
         raise PointlessConcept("Connectivity is undefined for the null graph.")
-    return _plain_bfs_bidirectional(G, next(iter(G))).nvals == len(G)
+    return _bfs_plain_bidirectional(G, next(iter(G))).nvals == len(G)

graphblas_algorithms/algorithms/shortest_paths/weighted.py

@@ -1,12 +1,13 @@
 import numpy as np
-from graphblas import Matrix, Vector, binary, monoid, replace, select, unary
+from graphblas import Matrix, Vector, binary, indexunary, monoid, replace, select, unary
 from graphblas.semiring import any_pair, min_plus
 
-from .._bfs import _bfs_level, _bfs_levels
+from .._bfs import _bfs_level, _bfs_levels, _bfs_parent, _bfs_plain
 from ..exceptions import Unbounded
 
 __all__ = [
     "single_source_bellman_ford_path_length",
+    "bellman_ford_path",
     "bellman_ford_path_lengths",
     "negative_edge_cycle",
 ]
@@ -164,6 +165,117 @@ def bellman_ford_path_lengths(G, nodes=None, *, expand_output=False):
     return D
 
 
+def _reconstruct_path_from_parents(G, parents, src, dst):
+    indices, values = parents.to_coo(sort=False)
+    d = dict(zip(indices.tolist(), values.tolist()))
+    if dst not in d:
+        return []
+    cur = dst
+    path = [cur]
+    while cur != src:
+        cur = d[cur]
+        path.append(cur)
+    return G.list_to_keys(reversed(path))
+
+
+def bellman_ford_path(G, source, target):
+    src_id = G._key_to_id[source]
+    dst_id = G._key_to_id[target]
+    if G.get_property("is_iso"):
+        # If the edges are iso-valued (and positive), then we can simply do level BFS
+        is_negative = G.get_property("has_negative_edges+")
+        if not is_negative:
+            p = _bfs_parent(G, source, target=target)
+            return _reconstruct_path_from_parents(G, p, src_id, dst_id)
+        raise Unbounded("Negative cycle detected.")
+    A, is_negative, has_negative_diagonal = G.get_properties(
+        "offdiag has_negative_edges- has_negative_diagonal"
+    )
+    if A.dtype == bool:
+        # Should we upcast e.g. INT8 to INT64 as well?
+        dtype = int
+    else:
+        dtype = A.dtype
+    cutoff = None
+    n = A.nrows
+    d = Vector(dtype, n, name="bellman_ford_path_length")
+    d[src_id] = 0
+    p = Vector(int, n, name="bellman_ford_path_parent")
+    p[src_id] = src_id
+
+    prev = d.dup(name="prev")
+    cur = Vector(dtype, n, name="cur")
+    indices = Vector(int, n, name="indices")
+    mask = Vector(bool, n, name="mask")
+    B = Matrix(dtype, n, n, name="B")
+    Indices = Matrix(int, n, n, name="Indices")
+    cols = prev.to_coo(values=False)[0]
+    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(prev @ A)
+        if cutoff is not None:
+            cur << select.valuele(cur, cutoff)
+
+        # 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
+        if not is_negative:
+            # Limit exploration if we have a target
+            cutoff = cur.get(dst_id, cutoff)
+
+        # Now try to find the parents!
+        # This is also not standard. Typically, UDTs and UDFs are used to keep
+        # track of both the minimum element and the parent id at the same time.
+        # Only include rows and columns that were used this iteration.
+        rows = cols
+        cols = cur.to_coo(values=False)[0]
+        B.clear()
+        B[rows, cols] = A[rows, cols]
+
+        # Reverse engineer to determine parent
+        B << binary.plus(prev & B)
+        B << binary.iseq(B & cur)
+        B << select.valuene(B, False)
+        Indices << indexunary.rowindex(B)
+        indices << Indices.reduce_columnwise(monoid.min)
+        p(indices.S) << indices
+        prev, cur = cur, prev
+    else:
+        # Check for negative cycle when for loop completes without breaking
+        cur << min_plus(prev @ A)
+        if cutoff is not None:
+            cur << select.valuele(cur, cutoff)
+        mask << binary.lt(cur & d)
+        if mask.get(dst_id):
+            raise Unbounded("Negative cycle detected.")
+    path = _reconstruct_path_from_parents(G, p, src_id, dst_id)
+    if has_negative_diagonal and path:
+        mask.clear()
+        mask[G.list_to_ids(path)] = True
+        diag = G.get_property("diag", mask=mask.S)
+        if diag.nvals > 0:
+            raise Unbounded("Negative cycle detected.")
+        mask << binary.first(mask & cur)  # mask(cur.S, replace) << mask
+        if mask.nvals > 0:
+            # Is there a path from any visited node with negative self-loop to target?
+            # We could actually stop as soon as any from `path` is visited
+            indices, _ = mask.to_coo(values=False)[0]
+            q = _bfs_plain(G, target=target, index=indices, cutoff=_i)
+            if dst_id in q:
+                raise Unbounded("Negative cycle detected.")
+    return path
+
+
 def negative_edge_cycle(G):
     # TODO: use a heuristic to try to stop early
     if G.is_directed():

graphblas_algorithms/generators/ego.py

@@ -1,4 +1,4 @@
-from ..algorithms.components.connected import _plain_bfs
+from ..algorithms.components.connected import _bfs_plain
 from ..algorithms.shortest_paths.weighted import single_source_bellman_ford_path_length
 
 __all__ = ["ego_graph"]
@@ -14,7 +14,7 @@ def ego_graph(G, n, radius=1, center=True, undirected=False, is_weighted=False):
     if is_weighted:
         v = single_source_bellman_ford_path_length(G2, n, cutoff=radius)
     else:
-        v = _plain_bfs(G2, n, cutoff=radius)
+        v = _bfs_plain(G2, n, cutoff=radius)
     if not center:
         del v[G._key_to_id[n]]
 

graphblas_algorithms/interface.py

@@ -83,6 +83,7 @@ class Dispatcher:
         nxapi.shortest_paths.unweighted.single_target_shortest_path_length
     )
     all_pairs_shortest_path_length = nxapi.shortest_paths.unweighted.all_pairs_shortest_path_length
+    bellman_ford_path = nxapi.shortest_paths.weighted.bellman_ford_path
     all_pairs_bellman_ford_path_length = (
         nxapi.shortest_paths.weighted.all_pairs_bellman_ford_path_length
     )

graphblas_algorithms/nxapi/shortest_paths/weighted.py

@@ -6,6 +6,7 @@
 
 __all__ = [
     "all_pairs_bellman_ford_path_length",
+    "bellman_ford_path",
     "negative_edge_cycle",
     "single_source_bellman_ford_path_length",
 ]
@@ -55,6 +56,15 @@ def single_source_bellman_ford_path_length(G, source, weight="weight"):
     return G.vector_to_nodemap(d)
 
 
+def bellman_ford_path(G, source, target, weight="weight"):
+    # TODO: what if weight is a function?
+    G = to_graph(G, weight=weight)
+    try:
+        return algorithms.bellman_ford_path(G, source, target)
+    except KeyError as e:
+        raise NodeNotFound(*e.args) from e
+
+
 def negative_edge_cycle(G, weight="weight", heuristic=True):
     # TODO: what if weight is a function?
     # TODO: use a heuristic to try to stop early