test_cycle

flower_snarks.py

@@ -335,6 +335,13 @@ Petersen = Gadget.join(
 )
 
 
+def sun(k):
+  return Gadget.join(
+    [ CUBIC_VERTEX ] * k,
+    [ ((i + 1, 2), ((i+1) % k + 1, 1)) for i in range(k) ],
+    [ (i + 1, 3) for i in range(k) ]
+  )
+
 
 def count_cdc_naive(G):
   assert(G.degree() == [3]*G.num_verts())

test_cycle.py

+from flower_snarks import *
+from sage.all import *
+
+def solve_gadget(g, alt_gadgets):
+  N = g.size()
+
+  P = MixedIntegerLinearProgram(maximization=False)
+  V = P.new_variable(real=True, nonnegative=True)
+
+  BOUNDARIES = list(CircuitDoubleCover.enumerate_boundaries(N))
+
+  def fake_gadget(b):
+    return FakeGadget(N, [ Boundary(b, 1) ])
+
+  def join(a, b):
+    return Gadget.join([ a, b ], [ ((1, i), (2, i)) for i in range(1,N+1) ], [])
+
+  def gadget_to_poly(gadget):
+    return sum(
+      V[b] * join(fake_gadget(b), gadget).eval(CircuitDoubleCover)
+      for b in BOUNDARIES
+    )
+
+  def gadget_to_constraint(gadget):
+    poly = gadget_to_poly(gadget)
+    n = gadget.eval(UnderlayingGraph)[0].value.num_verts()
+
+    P.add_constraint(poly >= 2**(n // 2))
+
+  for ag in alt_gadgets: gadget_to_constraint(ag)
+
+  P.set_objective(gadget_to_poly(g))
+
+  return (floor(P.solve()), 2**(g.eval(UnderlayingGraph)[0].value.num_verts()//2))
+
+G4 = [
+  Gadget.join([CUBIC_VERTEX] * 2, [((1,1), (2,1))], [ (1,2), (1,3), (2,2), (2,3) ]),
+  Gadget.join([CUBIC_VERTEX] * 2, [((1,1), (2,1))], [ (1,2), (2,2), (1,3), (2,3) ]),
+  Gadget.join([CUBIC_VERTEX] * 2, [((1,1), (2,1))], [ (1,2), (2,2), (2,3), (1,3) ]),
+]
+
+G4f = [
+  Gadget.join([FREE_EDGE]*2, [], [ (1,1), (1,2), (2,1), (2,2) ]),
+  Gadget.join([FREE_EDGE]*2, [], [ (1,1), (2,1), (1,2), (2,2) ]),
+  Gadget.join([FREE_EDGE]*2, [], [ (1,1), (2,1), (2,2), (1,2) ]),
+]
+
+G5 = [
+  Gadget.join([CUBIC_VERTEX] * 3, [((1,1), (2,1)), ((2,2), (3,2))], [ (1,2), (1,3), (2,3), (3,1), (3,3) ]),
+]
+
+print(solve_gadget(sun(5), G5))
+