Implement force-forward edges in baharev.

This may lead to upper-bound inconsistencies, thus we need a
force-forward implementation in eades, as well.

src/macrogen/fes.py

@@ -1,7 +1,7 @@
 # -*- coding: utf-8 -*-
 import itertools
 from collections import defaultdict
-from typing import Tuple, List, Generator, TypeVar, Iterable, Sequence
+from typing import Tuple, List, Generator, TypeVar, Iterable, Sequence, Optional
 from .config import config
 import networkx as nx
 import numpy as np
@@ -167,7 +167,7 @@ class FES_Baharev:
         http://www.mat.univie.ac.at/~neum/ms/minimum_feedback_arc_set.pdf.
     """
 
-    def __init__(self, graph: nx.DiGraph):
+    def __init__(self, graph: nx.DiGraph, force_forward_edges: Optional[List[Tuple[V, V]]] = None):
         self.original_graph = graph
         self.logger = config.getLogger(__name__ + '.' + self.__class__.__name__)
 
@@ -188,10 +188,15 @@ def __init__(self, graph: nx.DiGraph):
             weights.append(w)
             edges.append((u, v))
 
+        if force_forward_edges is None:
+            force_forward_edges = []
+
         self.graph = G
         self.weights = np.array(weights)
         self.edges = edges
         self.m = len(self.edges)
+        self.force_forward_edges = force_forward_edges
+        self.force_forward_vec = self.edge_vector(force_forward_edges)
         self.solver_args = {}
         self.solution_vector = None
         self.solution = None
@@ -277,6 +282,7 @@ def solve(self):
 
             cycle_vectors = [self.edge_vector(nx.utils.pairwise(cycle)) for cycle in simple_cycles]
             constraints = [cp.sum(a * y) >= 1 for a in cycle_vectors]
+            constraints.append(cp.sum(y * self.force_forward_vec) == 0)  # no force forward vec may be in the result set
             problem = cp.Problem(objective, constraints)
             resolution = problem.solve(**self.solver_args)
             if problem.status != 'optimal':

tests/test_fes.py

@@ -33,3 +33,17 @@ def test_baharev(graph1):
     solver = FES_Baharev(graph1)
     result = solver.solve()
     assert set(result) == {(3, 2)} or set(result) == {(2, 3)}
+
+
+def test_baharev_ff():
+    g = nx.DiGraph()
+    g.add_path([1, 2, 3, 4, 5], weight=1)
+    g.add_edge(3, 2, weight=2)
+
+    # This would normally remove (2,3) since its more lightweight than (3,2):
+    result = FES_Baharev(g).solve()
+    assert set(result) == {(2, 3)}
+
+    # However, when we forbid this, the next best solution will occur:
+    result = FES_Baharev(g, [(2, 3)]).solve()
+    assert set(result) == {(3, 2)}