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https://issues.apache.org/jira/browse/MAHOUT-710?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13128134#comment-13128134
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Sebastian Schelter commented on MAHOUT-710:
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I'm a bit undecided on this one.
We implemented triangle enumeration as a preprocessing step like it is
described in the article that Tillmann referenced but when we tried it on
medium sized graphs (100M edges) the performance was horrible...
It would be tragic to let the work Tillmann and Sebastian A. put in here go to
waste, but the algorithm as it is described in the article is clearly not
suited for production systems...
> Implementing K-Trusses
> ----------------------
>
> Key: MAHOUT-710
> URL: https://issues.apache.org/jira/browse/MAHOUT-710
> Project: Mahout
> Issue Type: New Feature
> Components: Graph
> Affects Versions: 0.5
> Reporter: Tillmann Fiehn
> Assignee: Sebastian Schelter
> Fix For: 0.6
>
> Attachments:
> 0001-SimplifyGraph_AugmentEdgesWithDegrees_EnumerateTriangles_workfine.patch,
> 0002-FindComponents_FindKTrusses_workfine.patch
>
> Original Estimate: 672h
> Remaining Estimate: 672h
>
> We are Tillmann Fiehn and Sebastian Arnold, IT students from TU Berlin. As
> Sebastian Schelter already announced, we are atteding Isabel's and
> Sebastian's class "Large scale data analysis and data mining" and picked an
> interesting project that we want to implement in Mahout. We are open for any
> hints and suggestions and would appreciate if you could share your thoughts
> on our proposal.
> Our goal is to implement a map/reduce algorithm for finding k-trusses in a
> given graph. A k-truss is a nontrivial, single-component maximal subgraph,
> such that every edge is contained in at least k-2 triangles in the subgraph.
> The algorithm was proposed in the IEEE paper J. Cohen 2009: "Graph Twiddling
> in a MapReduce World"
> (http://www.csee.usf.edu/~anda/CIS6930-S11/papers/graph-processing-w-mapreduce.pdf)
> and involves a number of graph algorithms that are to our knowledge
> currently not present in Mahout:
> *Goal: finding K-Trusses*
> * relaxation of k-member clique
> * non-trivial, single-component maximal subgraph, s.t.
> * every edge is contained in at least k-2 triangles in the subgraph
> *Algorithms to be implemented on top of Mahout / Hadoop:*
> *simplifyGraph*: Edges -> RepresentativeEdges
> * removes Loops (not cycles)
> * aggregate duplicate edges
> *augmentGraphWithDegrees*: RepresentativeEdges -> AugmentedEdges = (Edge (v,
> u) , d(v), d(u))
> * augements the edges with degree information for both nodes d(v) = |{E | E =
> (x,y) a. (x = v o. y = v) }|
> *enumerateTriangles*: AugmentedEdges = (Edge, d(v), d(u)) -> Triangles (v,
> u, s)
> * finds all triangles in a Graph
> *findComponents*: RepresentativeEdges -> ZoneAssignments (v, z)
> * finds all components of a graph, each identified as the order number of the
> lowest-order vertex contained
> * consists of:
> ** step 1: find adjacent zones: Edges x Zones -> InterzoneEdges (z, z)
> ** step 2: merge adjacent zones into one (the lowest-order neighbouring
> zone): InterzoneEdges, ZoneAssignments (v, z) -> Pairs (v, z)
> {noformat}
> while true do:
> step 1
> if empty set interzone edges break;
> step 2
> done
> {noformat}
> *findKTrusses*: Edges, k -> ZoneAssignments (v, z)
> * finds all k-trusses of the graph
> * each returned vertex v is part of a truss z
> {noformat}
> simplifyGraph
> while true do:
> augmentGraphWithDegrees
> enumerateTriangles
> keep only edges contained in k-2 triangles
> if all edges kept break;
> done
> findComponents
> {noformat}
> We suppose to create the package {{org.apache.mahout.graph.trusses}} and
> {{org.apache.mahout.graph.components}} in the {{core}} module.
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