private void MakeConnections(
Supernode[,] superNodes,
Supernode[] nodes,
int columnOffset,
int nextRow,
bool toFirstHalf,
int minLimit,
int maxLimit,
int D)
{
if (nextRow >= netHeight)
{
return;
}
var halfLen = nodes.Length / 2;
var nextRowFirstHalf = new Supernode[halfLen];
var nextRowSecondHalf = new Supernode[halfLen];
for (int i = 0; i < halfLen; i++)
{
nextRowFirstHalf[i] = superNodes[nextRow, columnOffset + i];
nextRowSecondHalf[i] = superNodes[nextRow, halfLen + columnOffset + i];
}
for (int i = 0; i < halfLen; i++)
{
if (CheckSuperNodeSize(nodes[i], nextRowSecondHalf[i], minLimit, maxLimit))
{
nodes[i].ConnectRight(nextRowSecondHalf[i], D);
}
if (CheckSuperNodeSize(nodes[halfLen + i], nextRowFirstHalf[i], minLimit, maxLimit))
{
nodes[halfLen + i].ConnectLeft(nextRowFirstHalf[i], D);
}
}
for (int i = 0; i < nodes.Length; i++)
{
if (CheckSuperNodeSize(nodes[i], superNodes[nextRow, columnOffset + i], minLimit, maxLimit))
{
if (nodes[i].LowerLeft == null)
{
nodes[i].ConnectLeft(superNodes[nextRow, columnOffset + i], D);
}
else
{
nodes[i].ConnectRight(superNodes[nextRow, columnOffset + i], D);
}
}
}
MakeConnections(superNodes, nextRowFirstHalf, columnOffset,
nextRow + 1, false, minLimit, maxLimit, D);
MakeConnections(superNodes, nextRowSecondHalf, columnOffset + halfLen,
nextRow + 1, true, minLimit, maxLimit, D);
}
private List <Supernode[]> HashBottomSuperNodes <T>(List <T> dataItems, int B)
{
var outputList = new List <Supernode[]>();
var lastRowIndex = netHeight - 1;
foreach (var dataItem in dataItems)
{
var hashSuperNodes = new Supernode[B];
var randomHash = new Random(dataItem.GetHashCode());
for (int i = 0; i < B; i++)
{
hashSuperNodes[i] = supernodes[lastRowIndex, randomHash.Next(0, netWidth)];
}
outputList.Add(hashSuperNodes);
}
return(outputList);
}
private void MakeConnections(Supernode[,] superNodes, int n, int C, int D, double alpha, double beta)
{
if (Math.Log(netWidth, 2) != Math.Truncate(Math.Log(netWidth, 2)))
{
throw new Exception("Number of rows must be a power of two!");
}
var minLimit = (int)Math.Round(alpha * C * Math.Log(n, Math.E));
var maxLimit = (int)Math.Round(beta * C * Math.Log(n, Math.E));
var firstRow = new Supernode[netWidth];
for (int i = 0; i < netWidth; i++)
{
firstRow[i] = superNodes[0, i];
}
MakeConnections(superNodes, firstRow, 0, 1, false, minLimit, maxLimit, D);
}
private void bn_InitializationFinished(Supernode[,] supernodes)
{
// draw the network
var g = new Graph();
var numRows = supernodes.GetLength(0);
var numCols = supernodes.GetLength(1);
int x, y = 50;
for (int i = 0; i < numRows; i++)
{
x = 30;
for (int j = 0; j < numCols; j++)
{
var node = supernodes[i, j];
g.AddNode(new GraphNode(node.Id.ToString(), x, y));
x += 40;
}
y += 95;
}
for (int i = 0; i < numRows; i++)
{
for (int j = 0; j < numCols; j++)
{
var superNode = supernodes[i, j];
if (superNode.LowerNodes.Length > 0)
{
foreach (var lowerNode in superNode.LowerNodes)
{
g.AddEdge(superNode.Id.ToString(), lowerNode.Id.ToString());
}
}
}
}
graphViewer.GraphSize = 33;
graphViewer.Graph = g;
graphViewer.Refresh();
}
private void MakeExpanderGraph(Supernode toSupernode, int D)
{
// construct the expander graph
foreach (var nodeId in NodeIds)
{
var toNodeIds = new List <int>();
foreach (var toNodeId in randUtils.PickRandomElements(toSupernode.NodeIds, D))
{
toNodeIds.Add(toNodeId);
}
if (AddNodeConnection != null)
{
AddNodeConnection(new KeyValuePair <int, NodeConnection>(nodeId,
new DownNodeConnection(this.Id, toSupernode.Id, toNodeIds)));
foreach (var toNodeId in toNodeIds)
{
AddNodeConnection(new KeyValuePair <int, NodeConnection>(toNodeId,
new UpNodeConnection(toSupernode.Id, this.Id, nodeId)));
}
}
}
}
/// <summary>
/// Connects the supernode to another supernode and constructs a random
/// constant-degree expander graph between the two sets of nodes.
/// </summary>
/// <param name="toNode"></param>
/// <param name="D">The degree of the constant-degree expander graph.</param>
public void ConnectRight(Supernode toNode, int D)
{
LowerRight = toNode;
MakeExpanderGraph(toNode, D);
}
/// <summary>
/// Builds the butterfly network.
/// </summary>
/// <param name="n">Total number of nodes.</param>
/// <param name="C">Every node chooses at random C top supernodes, C bottom supernodes, and Clog(n) middle supernodes to which each the node belongs.</param>
/// <param name="D">The degree of the random expander graph constructed between two supernodes.</param>
/// <param name="alpha">An expander graph maybe constructed between two supernodes if both are of size at least alpha*C*ln(n) and no more than beta*C*ln(n).</param>
/// <param name="beta">An expander graph maybe constructed between two supernodes if both are of size at least alpha*C*ln(n) and no more than beta*C*ln(n).</param>
internal void Initialize(IEnumerable <int> nodeIds, int n, int B, int C, int D, int T, double alpha, double beta)
{
IsInitialized = false;
this.n = n;
this.B = B;
this.T = T;
this.beta = beta;
var netWidthTemp = n / Math.Log(n, 2);
// round this to the nearest greater power of two
netWidth = (int)Math.Pow(2.0, Math.Ceiling(Math.Log(netWidthTemp, 2)));
netHeight = (int)Math.Log(netWidth, 2) + 1;
supernodes = new Supernode[netHeight, netWidth];
for (int i = 0; i < netHeight; i++)
{
for (int j = 0; j < netWidth; j++)
{
supernodes[i, j] = new Supernode(i * netWidth + j, randUtils);
supernodes[i, j].AddNodeConnection +=
new Supernode.AddNodeConnectionHandler(CollectNodeConnections);
}
}
// construct the network
nodeConnections = new Dictionary <int, SetupMessageData>();
RegisterNodes(nodeIds, supernodes, C);
MakeConnections(supernodes, n, C, D, alpha, beta);
// each node should also point to T top supernodes
foreach (var nodeId in nodeIds)
{
var topSupernodeIds = randUtils.GetRandomPerm(0, netWidth, T);
foreach (var topSupernodeId in topSupernodeIds)
{
var topSupernode = supernodes[0, topSupernodeId];
// -1 means the node is directly connected to a supernode
// without belonging to any supernode
CollectNodeConnections(
new KeyValuePair <int, NodeConnection>(nodeId,
new DownNodeConnection(-1, topSupernodeId, topSupernode.NodeIds)));
foreach (var topNodeId in topSupernode.NodeIds)
{
// -1 means topNode is connected to an individual node (nodeId) that
// doesn't belong to any supernode
CollectNodeConnections(
new KeyValuePair <int, NodeConnection>(topNodeId,
new UpNodeConnection(topSupernode.Id, -1, nodeId)));
}
}
}
//// send the network setup information to nodes
//foreach (var nodeId in nodeIds)
//{
// var msg = new SetupMessage(netHeight, netWidth, B, nodeConnections[nodeId]);
// Send(nodeId, msg, 100);
//}
IsInitialized = true;
if (InitFinished != null)
{
InitFinished(supernodes);
}
}
private bool CheckSuperNodeSize(Supernode node1, Supernode node2, int min, int max)
{
return(node1.Size >= min && node1.Size <= max &&
node2.Size >= min && node2.Size <= max);
}
private void MakeExpanderGraph(Supernode toSupernode, int D)
{
// construct the expander graph
foreach (var nodeId in NodeIds)
{
var toNodeIds = new List<int>();
foreach (var toNodeId in randUtils.PickRandomElements(toSupernode.NodeIds, D))
toNodeIds.Add(toNodeId);
if (AddNodeConnection != null)
{
AddNodeConnection(new KeyValuePair<int, NodeConnection>(nodeId,
new DownNodeConnection(this.Id, toSupernode.Id, toNodeIds)));
foreach (var toNodeId in toNodeIds)
{
AddNodeConnection(new KeyValuePair<int, NodeConnection>(toNodeId,
new UpNodeConnection(toSupernode.Id, this.Id, nodeId)));
}
}
}
}
/// <summary>
/// Connects the supernode to another supernode and constructs a random
/// constant-degree expander graph between the two sets of nodes.
/// </summary>
/// <param name="toNode"></param>
/// <param name="D">The degree of the constant-degree expander graph.</param>
public void ConnectRight(Supernode toNode, int D)
{
LowerRight = toNode;
MakeExpanderGraph(toNode, D);
}
