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# Graphs

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### Graphs

1. 1. Graph Algorithms and MapReduce Paolo Castagna The words and opinions expressed here are my own, and do not, in any way, represent the views of my employer.
2. 2. Why graphs ?
3. 3. I am an infornographer ! see: http://en.wikipedia.org/wiki/Infornography
4. 4. ... addicted to RDF
5. 5. RDF is (just) a directed labeled multigraph
6. 6. RDF is (just) a directed labeled multigraph
7. 7. RDF is (just) a directed labeled multigraph URI2 URI1 URI3
8. 8. RDF is (just) a directed labeled multigraph URI2 URI1 URI3 URI4
9. 9. RDF processing
10. 10. RDF parallel processing
11. 11. MapReduce ?
12. 12. “ ... almost no descriptions of graph algorithms appear in the literature, with the exception of a simplified PageRank calculation and a naive implementation of finding distances from a specified node. ” Graph Twiddling in a MapReduce World, Jonathan Cohen
13. 13. RDF processing Inference1 (?x p ?y) (?y q r) -> (?x rdf:type t) (?x p ?y) (?y p ?z) -> (?x p ?z) 1 using a rule engine with forward rules only and a total materialization strategy
14. 14. Transitive closure
15. 15. Transitive closure
16. 16. MapReduce ?
17. 17. Transitive closure 1: 4, 6, 7 1: 4, 6, 7 2: 5 map 3: 2, 4, 7 1, >4 4: 1, 3, 6 1, >6 5: 2, 3 1, >7 6: 5 4, <1 6, <1 7: 3, 5 7, <1
18. 18. Transitive closure 1: 4, 6, 7 6, <1 2: 5 6, <4 3: 2, 4, 7 6, >5 4: 1, 3, 6 5: 2, 3 reduce 6: 5 1: 5 7: 3, 5 4: 5
19. 19. Transitive closure WARNINGS: - Thinking in progress ! - Not implemented (yet) ! - Stop when no new edges are found
20. 20. Transitive reduction
21. 21. Transitive reduction
22. 22. MapReduce ?
23. 23. PageRank Lessons learned