#### Description

First of all, sorry for the long explanation to this feature.

I want to expand the API of Giraph with a new function called master.compute(), that would get called at the master before each superstep and I will try to explain the purpose that it would serve with an example. Let's say we want to implement the following simplified version of the k-means clustering algorithm. Pseudocode below:

- Input G(V, E), k, numEdgesThreshold, maxIterations
- Algorithm:
- int numEdgesCrossingClusters = Integer.MAX_INT;
- int iterationNo = 0;
- while ((numEdgesCrossingCluster > numEdgesThreshold) && iterationNo < maxIterations)
{
* iterationNo++;
* int[] clusterCenters = pickKClusterCenters(k, G);
* findClusterCenters(G, clusterCenters);
* numEdgesCrossingClusters = countNumEdgesCrossingClusters();
* }
The algorithm goes through the following steps in iterations:

1) Pick k random initial cluster centers

2) Assign each vertex to the cluster center that it's closest to (in Giraph, this can be implemented in message passing similar to how ShortestPaths is implemented):

3) Count the nuimber of edges crossing clusters

4) Go back to step 1, if there are a lot of edges crossing clusters and we haven't exceeded maximum number of iterations yet.

In an algorithm like this, step 2 and 3 are where most of the work happens and both parts have very neat message-passing implementations. I'll try to give an overview without going into the details. Let's say we define a Vertex in Giraph to hold a custom Writable object that holds 2 integer values and sends a message with upto 2 integer values.

Step 2 is very similar to ShortestPaths algorithm and has two stages: In the first stage, each vertex checks to see whether or not it's one of the cluster centers. If so, it assigns itself the value (id, 0), otherwise it assigns itself (Null, Null). In the 2nd stage, the vertices assign themselves to the minimum distance cluster center by looking at their neighbors (cluster centers, distance) values (received as 2 integer messages) and their current values, and changing their values if they find a lower distance cluster center. This happens in x number of supersteps until every vertex converges.

Step 3, counting the number of edges crossing clusters, is also very easy to implement in Giraph. Once each vertex has a cluster center, the number of edges crossing clusters can be counted by an aggregator, let's say called "num-edges-crossing". It would again have two stages: First stage, every vertex just sends its cluster id to all its neighbors. Second stage, every vertex looks at their neighbors' cluster ids in the messages, and for each cluster id that is not equal to its own cluster id, it increments "num-edges-crossing" by 1.

The other 2 steps, step 1 and 4, are very simple sequential computations. Step 1 just picks k random vertex ids and puts it into an aggregator. Step 4 just compares "num-edges-crossing" by a threshold and also checks whether or not the algorithm has exceeded maxIterations (not supersteps but iterations of going through Steps 1-4). With the current API, it's not clear where to do these computations. There is a per worker function preSuperstep() that can be implemented, but if we decide to pick a special worker, let's say worker 1, to pick the k vertices then we'd waste an entire superstep where only worker 1 would do work, (by picking k vertices in preSuperstep() and put them into an aggregator), and all other workers would be idle. Trying to do this in worker 1 in postSuperstep() would not work either because, worker 1 needs to know that all the vertices have converged to understand that it's time to pick k vertices or it's time do check in step 4, which would only be available to it in the beginning of the next superstep.

A master.compute() extension would run at the master and before the superstep and would modify the aggregator that would keep the k vertices before the aggregators are broadcast to the workers, which are all very short sequential computations, so they would not waste resources the way a preSuperstep() or postSuperstep() approach would do. It would also enable running new algorithms like kmeans that are composed of very vertex-centric computations glued together by small sequential ones. It would basically boost Giraph with sequential computation in a non-wasteful way.

I am a phd student at Stanford and I have been working on my own BSP/Pregel implementation since last year. It's called GPS. I haven't distributed it, mainly because in September I learned about Giraph and I decided to slow down on working on it . We have basically been using GPS as our own research platform. The source code for GPS is here if any one is interested (https://subversion.assembla.com/svn/phd-projects/gps/trunk/). We have the master.compute() feature in GPS, and here's an example of KMeans implementation in GPS with master.compute(): (https://subversion.assembla.com/svn/phd-projects/gps/trunk/src/java/gps/examples/kmeans/). (Aggregators are called GlobalObjects in GPS). There is another example (https://subversion.assembla.com/svn/phd-projects/gps/trunk/src/java/gps/examples/randomgraphcoarsening/), which I'll skip explaining because it's very detailed and would make the similar points that I am trying to make with k-means. Master.compute() in general would make it possible to glue together any graph algorithm that is composed of multiple stages with different message types and computations that is conducive to run with vertex.compute(). There are many examples of such algorithms: recursive partitioning, triangle counting, even much simpler things like finding shortests paths for 100 vertices in pieces (first to 5 vertices, then to another 5, then to another 5, etc..), which would be good because trying to find shortests paths to 100 vertices require a very large messages (would need to store 100 integers per message)).

If the Giraph team approves, I would like to take a similar approach in implementing this feature in Giraph as I've done in GPS. Overall:

Add a Master.java to org.apache.giraph.graph, that is default Master, with a compute function that by default aggregates all aggregators and does the check of whether or not the computation has ended (by comparining numVertices with numFinishedVertices). This would be a refactoring of org.apache.giraph.graph.BspServiceMaster class (as far as I can see).

Extend GiraphJob to have a setMaster() method to set a master class (by default it would be the default master above)

The rest would be sending the custom master class to probably all workers but only the master would instantiate it with reflection. I need to learn more on how to do these, I am not familiar with that part of the Giraph code base yet.