1. Design Patterns for Efficient Graph Algorithms in MapReduce Jimmy Lin and Michael Schatz (Slides by Tyler S. Randolph)

2. What is MapReduce? Definition: Programming model and an associated implementation for processing and generating large datasets with a parallel, distributed algorithm on a cluster 2 main parts - Mapper - Reducer 2 sub parts - Combiner - Partitioner

3. What is MapReduce? 1)Mappers applied to input 2)Combiners perform local aggregation 3)Partitioners send data to reducers 4)Reducers aggregate results Very parallelizable

4. Example Step through the MapReduce function to return the # of times a certain word length appears in the following sentence: We should all take summer classes this year. Write and label the outputs of the mapper, combiner, and reducer (no need for a partitioner with an example this small)

5. Example (continued) “We should all take summer classes this year.” Mapper- 2: We 5: should 3: all 4: take 6: summer 7: classes 4: this 4: year

6. Example (continued) “We should all take summer classes this year.” Mapper- 2: We 3: all 4: take 4: this 4: year 5: should 6: summer 7: classes

7. Example (continued) “We should all take summer classes this year.” Combiner- 2: [We] 3: [all] 4: [take, this, year] 5: [should] 6: [summer] 7: [classes]

8. Example (continued) “We should all take summer classes this year.” Reducer- 2: 1 3: 1 4: 3 5: 1 7: 1

9. “Message Passing” Graphs G = (V, E) -Graph = (Vertices, Edges) -directed graphs In-degree - how many vertices point to me Out-degree - how many vertices do I point to Metadata

10. PageRank Definition: Google’s main algorithm that works by counting the number and quality of links to a page to determine a rough estimate of how important the website is. Assumption - Really one big popularity contest Graph Topology - “physical” layout of the graph - what points to what

11. PageRank At each iteration… - Computations occur at every vertex as a function of the vertex’s internal state and the LOCAL graph structure - Partial results in the form of messages are “passed” via DIRECTED edges to each vertex’s neighbors - Computations occur at every vertex based on incoming partial results, potentially altering the vertex’s internal state

12. PageRank

13. Basic PageRank Algorithm

14. Basic Example Say A has a link to B, B has links to C and A, C has a link to A, and D has a link to A B and C…

15. Basic Example (continued) Each page has starting rank of 0.25 PR(A) = (0.25 / L(B)) + (0.25 / L(C)) + (0.25 / L(D)) B has 2 links, C has 1 link, D has 3 links PR(A) = (0.25 / 2) + (0.25 / 1) + (0.25 / 3) PR(A) = = 0.4583…

16. Complications Need a way to deal with… - Random hops - Sinks

17. Dampening Factor Probability that at any step, the surfer will continue on as he has been 0.85 - (1 – 0.85) / N

18. Dampening Factor

19. Tying It All Together Why MapReduce - good for this type of calculation - Exploit shuffle and sort phase to aid info passing Parallelization of PageRank - Only care about local topology and dampening factor - No need to worry about entire picture - create adjacency list representation of the graph where key is id of vertex and value is vertex’s structure and metadata -metadata probably include out-degree and internal state

20. Bibliography "PageRank." Wikipedia. Wikimedia Foundation, 26 Apr. 2015. Web. 03 May 2015 "MapReduce." Wikipedia. Wikimedia Foundation, 01 May 2015. Web. 03 May 2015. Lin, Jimmy, and Michael Schatz. "Design Patterns for Efficient Graph Algorithms in MapReduce." Thesis. University of Maryland, College Park, 2010. Https://cs.wmich.edu. Web. 1 May 2015..

21. Questions?