Features/algorithm demo (#99)

* added algorithm demo

examples/algorithm_demo.py

@@ -0,0 +1,78 @@
+"""
+This file shows a visualization of the minorminer.find_embedding() algorithm.
+
+At each step of the find_embedding() algorithm, a new chain is inserted for a node in the source graph, where chains
+are allowed to overlap. After all chains have inserted, the algorithm iteratively removes and reinserts chains,
+attempting to minimize the amount of overlap between them. Eventually all overlap will be removed, and the result is
+a valid embedding.
+
+In this example, a complete graph K_8 is embedded into a chimera_graph C_2.
+
+"""
+
+from minorminer import miner
+import networkx as nx
+import dwave_networkx as dnx
+import matplotlib.pyplot as plt
+
+
+# Parameters of the demo
+wait_for_input = False                   # wait for user input to advance to the next step
+G = nx.complete_graph(8)                # source graph
+C = dnx.generators.chimera_graph(2)     # target graph
+
+
+def show_current_embedding(emb):
+    # visualize overlaps.
+    plt.clf()
+    dnx.draw_chimera_embedding(C, emb=emb, overlapped_embedding=True, show_labels=True)
+    plt.show()
+    if wait_for_input:
+        plt.pause(0.001)
+        input()
+    else:
+        plt.pause(1)
+
+
+def compute_bags(C, emb):
+    # Given an overlapped embedding, compute the set of source nodes embedded at every target node.
+    bags = {v: [] for v in C.nodes()}
+    for x, chain in emb.items():
+        for v in chain:
+            bags[v].append(x)
+    return bags
+
+
+# Run the algorithm.
+plt.ion()
+m = miner(G, C, random_seed=0)
+found = False
+emb = {}
+print("Embedding K_8 into Chimera C(2).")
+for iteration in range(3):
+    if iteration == 0:
+        print("\nInitialization phase...")
+    elif iteration==1:
+        print("\nOverfill improvement phase...")
+
+    for v in G.nodes():
+        if iteration > 0:
+            # show embedding with current vertex removed.
+            removal_emb = emb.copy()
+            removal_emb[v] = []
+            show_current_embedding(removal_emb)
+
+        # run one step of the algorithm.
+        emb = m.quickpass(varorder=[v], clear_first=False, overlap_bound=G.number_of_nodes())
+
+        # check if we've found an embedding.
+        bags = compute_bags(C, emb)
+        overlap = max(len(bag) for bag in bags.values())
+        if overlap==1 and iteration > 0 and not(found):
+            print("\nEmbedding found. Chain length improvement phase...")
+            found = True
+
+        show_current_embedding(emb)
+
+    max_chain_length = max(len(chain) for chain in emb.values())
+    print("\tIteration {}: max qubit fill = {}, max chain length = {}".format(iteration, overlap, max_chain_length))