Added Dinic's algorithm for maximum flow

Graph_Algorithms/src/Maximum_flow/Dinic_max_flow.py

@@ -0,0 +1,256 @@
+"""
+Code by BH4
+
+This file includes:
+  - Flow graph data structure
+  - Dinic's algorithm for max flow
+"""
+
+
+class Vertex():
+    def __init__(self, node):
+        """
+        adjacent has keys of other vertices with values being the weight of
+        the edge.
+        """
+
+        self.id = node
+        self.adjacent = {}
+
+    def add_neighbor(self, neighbor, capacity=0, flow=0):
+        self.adjacent[neighbor] = (flow, capacity)
+
+    def get_residual(self, node_B):
+        edge = self.adjacent[node_B]
+        return edge[1] - edge[0]
+
+    def get_flow(self, node_B):
+        if node_B not in self.adjacent:
+            return 0
+
+        edge = self.adjacent[node_B]
+        return edge[0]
+
+    def set_flow(self, node_B, flow):
+        edge = self.adjacent[node_B]
+        self.adjacent[node_B] = (flow, edge[1])
+
+    def get_capacity(self, node_B):
+        edge = self.adjacent[node_B]
+        return edge[1]
+
+    def set_capacity(self, node_B, capacity):
+        edge = self.adjacent[node_B]
+        self.adjacent[node_B] = (edge[0], capacity)
+
+    def get_neighbors(self):
+        return self.adjacent.keys()
+
+
+class Graph():
+    def __init__(self):
+        self.graph_dict = {}
+        self.source = None
+        self.sink = None
+
+    def add_vertex(self, node):
+        self.graph_dict[node] = Vertex(node)
+
+    def add_edge(self, start, end, capacity=0):
+        if start not in self.graph_dict:
+            self.add_vertex(start)
+        if end not in self.graph_dict:
+            self.add_vertex(end)
+
+        self.graph_dict[start].add_neighbor(end, capacity=capacity)
+
+    def create_directed_graph(self, sources, sinks, capacities):
+        """
+        We will replace all the sources with a single source and all the sinks
+        with a single sink to simplify the problem.
+
+        The source will be labeled -1 and the sink will be labeled -2 to avoid
+        collisions with names of other nodes.
+
+        Capacities should be given as a matrix. Each element capacities[A][B]
+        is the capacity available for the edge from A to B
+        """
+
+        for A in range(len(capacities)):
+            node_A = A
+            if A in sources:
+                node_A = -1
+            elif A in sinks:
+                node_A = -2
+            for B in range(len(capacities)):
+                node_B = B
+                if B in sources:
+                    node_B = -1
+                elif B in sinks:
+                    node_B = -2
+
+                # There is no reason to send bunnies to the same room.
+                if capacities[A][B] > 0 and node_A != node_B:
+                    if node_A in self.graph_dict and node_B in self.graph_dict[node_A].get_neighbors():
+                        tot_cap = self.graph_dict[node_A].get_capacity(node_B)+capacities[A][B]
+                        self.graph_dict[node_A].set_capacity(node_B, tot_cap)
+                    else:
+                        self.add_edge(node_A, node_B, capacity=capacities[A][B])
+
+        self.source = -1
+        self.sink = -2
+
+    def residual_graph(self):
+        G_f = Graph()
+
+        for node_A in self.graph_dict:
+            for node_B in self.graph_dict[node_A].get_neighbors():
+                c_f_AB = self.graph_dict[node_A].get_residual(node_B)
+                c_f_BA = self.graph_dict[node_A].get_flow(node_B)
+
+                if c_f_AB > 0:
+                    G_f.add_edge(node_A, node_B, capacity=c_f_AB)
+
+                if c_f_BA > 0:
+                    G_f.add_edge(node_B, node_A, capacity=c_f_BA)
+
+        if self.source in G_f.graph_dict:
+            G_f.source = self.source
+        if self.sink in G_f.graph_dict:
+            G_f.sink = self.sink
+        return G_f
+
+    def level_graph(self):
+        """
+        Use a bfs to define a level graph from the current graph.
+        """
+
+        G_L = Graph()
+
+        # used_verts is a dictionary of the distances of each node from the source
+        used_verts = dict()
+
+        queue = [(self.source, 0)]
+        used_verts[self.source] = 0
+        sink_distance = None
+        while len(queue) > 0:
+            curr, dist = queue.pop(0)
+
+            if sink_distance is None or dist < sink_distance:
+                # Don't add any vertices which are as far or farther from
+                # the source as the sink. Since they won't reach the sink.
+
+                for neighbor in self.graph_dict[curr].get_neighbors():
+                    c = self.graph_dict[curr].get_capacity(neighbor)
+
+                    if neighbor not in used_verts:
+                        queue.append((neighbor, dist+1))
+                        used_verts[neighbor] = dist+1
+
+                        G_L.add_edge(curr, neighbor, capacity=c)
+
+                        if neighbor is self.sink:
+                            sink_distance = dist+1
+                    else:
+                        if used_verts[neighbor] == dist+1:
+                            G_L.add_edge(curr, neighbor, capacity=c)
+
+        if self.source in G_L.graph_dict:
+            G_L.source = self.source
+        if self.sink in G_L.graph_dict:
+            G_L.sink = self.sink
+        return G_L, sink_distance
+
+    def send_flow(self, node, n=None):
+        if node == self.source:
+            # Needs to be a number larger than the maximum possible flow
+            n = 200000000000
+
+        if node == self.sink:
+            return n
+
+        tot_new_flow = 0
+        for neighbor in self.graph_dict[node].get_neighbors():
+            if n > 0:
+                to_send = self.graph_dict[node].get_residual(neighbor)
+                if to_send > n:
+                    to_send = n
+                actual_used = self.send_flow(neighbor, n=to_send)
+
+                already_sent = self.graph_dict[node].get_flow(neighbor)
+                self.graph_dict[node].set_flow(neighbor, actual_used+already_sent)
+                new_flow = actual_used
+                n -= new_flow
+                tot_new_flow += new_flow
+
+        return tot_new_flow
+
+    def blocking_flow(self):
+        self.send_flow(self.source)
+
+    def add_flow(self, other):
+        """
+        Given a second graph, for any edge from A to B in self add the flow of
+        the same edge from other.
+        """
+        for node_A in self.graph_dict:
+            for node_B in self.graph_dict[node_A].get_neighbors():
+                f_self = self.graph_dict[node_A].get_flow(node_B)
+                f_other = 0
+                f_other_reverse = 0
+                if node_A in other.graph_dict:
+                    f_other = other.graph_dict[node_A].get_flow(node_B)
+                if node_B in other.graph_dict:
+                    f_other_reverse = other.graph_dict[node_B].get_flow(node_A)
+
+                self.graph_dict[node_A].set_flow(node_B, f_self+f_other-f_other_reverse)
+
+    def sum_flow(self, node_A):
+        """
+        Return total flow leaving node_A
+        """
+
+        tot = 0
+        for node_B in self.graph_dict[node_A].get_neighbors():
+            tot += self.graph_dict[node_A].get_flow(node_B)
+
+        return tot
+
+
+def max_flow(G):
+    """
+    Implementation of Dinic's algorithm for calculating maximum flow.
+    """
+
+    G_f = G.residual_graph()
+    G_L, sink_distance = G_f.level_graph()
+
+    # The algorithm repeats until the level
+    while sink_distance is not None:
+        G_L.blocking_flow()
+        G.add_flow(G_L)
+
+        G_f = G.residual_graph()
+        G_L, sink_distance = G_f.level_graph()
+
+    return G.sum_flow(G.source)
+
+
+if __name__ == '__main__':
+    """
+    Defined here is a graph whose maximum flow is 19.
+
+    Example from https://en.wikipedia.org/wiki/Dinic%27s_algorithm#Algorithm
+    """
+    source = [0]
+    sink = [5]
+    capacities = [[0, 10, 10, 0, 0,  0],
+                  [0,  0,  2, 4, 8,  0],
+                  [0,  0,  0, 0, 9,  0],
+                  [0,  0,  0, 0, 0, 10],
+                  [0,  0,  0, 6, 0, 10],
+                  [0,  0,  0, 0, 0,  0]]
+
+    G = Graph()
+    G.create_directed_graph(source, sink, capacities)
+    print('Maximum flow through graph is {}'.format(max_flow(G)))