1. Large-scale file systems and Map-Reduce Single-node architecture Memory Disk CPU Google example: 20+ billion web pages x 20KB = 400+ Terabyte 1 computer reads 30-35 MB/sec from disk ~4 months to read the web ~1,000 hard drives to store the web Takes even more to do something useful with the data New standard architecture is emerging: Cluster of commodity Linux nodes Gigabit ethernet interconnect Slide based on www.mmds.com

2. Distributed File Systems Files are very large, read/append. They are divided into chunks. – Typically 64MB to a chunk. Chunks are replicated at several compute-nodes. A master (possibly replicated) keeps track of all locations of all chunks. Slide based on www.mmds.com

3. Commodity clusters: compute nodes Organized into racks. Intra-rack connection typically gigabit speed. Inter-rack connection faster by a small factor. Recall that chunks are replicated Some implementations: GFS (Google File System – proprietary). In Aug 2006 Google had ~450,000 machines HDFS (Hadoop Distributed File System – open source). CloudStore (Kosmix File System, open source). Slide based on www.mmds.com

4. Problems with Large-scale computing on commodity hardware Challenges: – How do you distribute computation? – How can we make it easy to write distributed programs? – Machines fail: One server may stay up 3 years (1,000 days) If you have 1,000 servers, expect to loose 1/day People estimated Google had ~1M machines in 2011 – 1,000 machines fail every day! Slide based on www.mmds.com

5. Issue: Copying data over a network takes time Idea: – Bring computation close to the data – Store files multiple times for reliability Map-reduce addresses these problems – Google’s computational/data manipulation model – Elegant way to work with big data – Storage Infrastructure – File system Google: GFS. Hadoop: HDFS – Programming model Map-Reduce

6. Slide based on www.mmds.com Problem: – If nodes fail, how to store data persistently? Answer: – Distributed File System: Provides global file namespace Google GFS; Hadoop HDFS; Typical usage pattern – Huge files (100s of GB to TB) – Data is rarely updated in place – Reads and appends are common

7. Racks of Compute Nodes File Chunks Replication Slide based on www.mmds.com

8. 3-way replication of files, with copies on different racks. Replication Slide based on www.mmds.com

9. Map-Reduce You write two functions, Map and Reduce. – They each have a special form to be explained. System (e.g., Hadoop) creates a large number of tasks for each function. – Work is divided among tasks in a precise way. Slide based on www.mmds.com

10. Map-Reduce Algorithms Map tasks convert inputs to key-value pairs. – “keys” are not necessarily unique. Outputs of Map tasks are sorted by key, and each key is assigned to one Reduce task. Reduce tasks combine values associated with a key. Slide based on www.mmds.com

11. Simple map-reduce example: Word Count We have a large file of words, one word to a line Count the number of times each distinct word appears in the file Sample application: analyze web server logs to find popular URLs Different scenarios: – Case 1: Entire file fits in main memory – Case 2: File too large for main mem, but all pairs fit in main mem – Case 3: File on disk, too many distinct words to fit in memory Slide based on www.mmds.com

12. Word Count Map task: For each word, e.g. CAT output (CAT,1) Total output: (w 1,1), (w 1,1), …., (w 1,1) (w 2,1), (w 2,1), …., (w 2,1) …… Hash each (w,1) to bucket h(w) in [0,r-1] in local intermediate file. r is the number of reducers Master: Group by key: (w 1,[1,1,…,1]), (w 2,[1,1,…,1]), Push group (w,[1,1,..,1]) to reducer h(w) Reduce task: Reducer h(w) Read : (w,[1,1,…,1]) Aggregate: each (w,[1,1,…,1]) into (w,sum) Output: (w,sum) into common output file Since addition is commutative and associative the map task could have sent : (w 1,sum 1 ), (w 2,sum 2 ), … Reduce task would receive: (w i,sum i,1 ), (w i,sum i,2 ), … (w j,sum j,1 ), (w j,sum j,2 ), … and output (w i,sum i ), (w j,sum j ), …. Slide based on www.mmds.com

13. Partition Function Inputs to map tasks are created by contiguous splits of input file For reduce, we need to ensure that records with the same intermediate key end up at the same worker System uses a default partition function e.g., hash(key) mod R Sometimes useful to override – E.g., hash(hostname(URL)) mod R ensures URLs from a host end up in the same output file Slide based on www.mmds.com

14. Coordination Master data structures – Task status: (idle, in-progress, completed) – Idle tasks get scheduled as workers become available – When a map task completes, it sends the master the location and sizes of its R intermediate files, one for each reducer – Master pushes this info to reducers Master pings workers periodically to detect failures Slide based on www.mmds.com

15. Data flow Input, final output are stored on a distributed file system – Scheduler tries to schedule map tasks “close” to physical storage location of input data Intermediate results are stored on local FS of map and reduce workers Output is often input to another map-reduce task Master data structures – Task status: (idle, in-progress, completed) – Idle tasks get scheduled as workers become available – When a map task completes, it sends the master the location and sizes of its R intermediate files, one for each reducer – Master pushes this info to reducers Master pings workers periodically to detect failures Slide based on www.mmds.com

16. Failures Map worker failure – Map tasks completed or in-progress at worker are reset to idle (result sits locally at worker) – Reduce workers are notified when task is rescheduled on another worker Reduce worker failure – Only in-progress tasks are reset to idle Master failure – Map-reduce task is aborted and client is notified Slide based on www.mmds.com

17. How many Map and Reduce jobs? M map tasks, R reduce tasks Rule of thumb: – Make M and R much larger than the number of nodes in cluster – One DFS chunk per map is common – Improves dynamic load balancing and speeds recovery from worker failure Usually R is smaller than M, because output is spread across R files Slide based on www.mmds.com

18. Relational operators with map-reduce Selection Map task: If C(t) is true output pair (t,t) Reduce task: With input (t,t) output t Selection is not really suitable for map-reduce, everything could have been done in the map task

19. Relational operators with map-reduce Projection Map task: Let t’ be the projection of t. Output pair (t’,t’) Reduce task: With input (t’,[t’,t’,…,t’] ) output t’ Here the duplicate elimination is done by the reduce task

20. Relational operators with map-reduce Union R  S Map task: for each tuple t of the chunk of R or S output (t, t) Reduce task: input is (t,[t]) or (t,[t, t]). Output t Intersection R  S Map task: for each tuple t of the chunk output (t,t) Reduce task: if input is (t,[t,t]), output t if input is (t,[t]), output nothing Difference R – S Map task: for each tuple t of R output (t,R) for each tuple t of S output (t,S) Reduce task: if input is (t,[R]), output t if input is (t,[R,S]), output nothing

21. Joining by Map-Reduce Suppose we want to compute R(A,B) JOIN S(B,C), using k Reduce tasks. – I.e., find tuples with matching B-values. R and S are each stored in a chunked file. Use a hash function h from B-values to k buckets. – Bucket = Reduce task. The Map tasks take chunks from R and S, and send: – Tuple R(a,b) to Reduce task h(b). Key = b value = R(a,b). – Tuple S(b,c) to Reduce task h(b). Key = b; value = S(b,c). Slide based on www.mmds.com

22. Reduce task i Map tasks send R(a,b) if h(b) = i Map tasks send S(b,c) if h(b) = i All (a,b,c) such that h(b) = i, and (a,b) is in R, and (b,c) is in S. Key point: If R(a,b) joins with S(b,c), then both tuples are sent to Reduce task h(b). Thus, their join (a,b,c) will be produced there and shipped to the output file. Slide based on www.mmds.com

23. Mapping tuples in joins Mapper for R(1,2) R(1,2)(2, (R,1)) Mapper for R(4,2) R(4,2) Mapper for S(2,3) S(2,3) Mapper for S(5,6) S(5,6) (2, (R,4)) (2, (S,3)) (5, (S,6)) 23 Reducer for B = 2 Reducer for B = 5 (2, [(R,1), (R,4), (S,3)]) (5, [(S,6)]) Slide based on www.mmds.com

24. Output of the Reducers Reducer for B = 2 Reducer for B = 5 (2, [(R,1), (R,4), (S,3)]) (5, [(S,6)]) (1,2,3), (4,2,3) Slide based on www.mmds.com

25. Relational operators with map-reduce Grouping and aggregation:  A,agg(B) (R(A,B,C)) Map task: for each tuple (a,b,c) output (a,[b]) Reduce task: if input is (a,[b 1, b 2, …, b n ]), output (a,agg(b 1, b 2, …, b n )) for example (a, b 1 +b 2 + …+b n )

26. Matrix-vector multiplication using map-reduce j=1

27. If vector doesn’t fit in main memory Divide matrix and vector into stripes: Each map task gets a chunk of stripe i of the matrix and the entire stripe i of the vector and produces pairs Reduce task i gets all pairs and produces pairs Slide based on www.mmds.com

28. Example: MAPPERS: REDUCERS:

29. Examples: Hamming distance 1 between bit-strings Matrix multiplication in one MR-round Matrix multiplication in two MR-rounds Three-way joins in two rounds and in one round

31. Relational operators with map-reduce Three-Way Join We shall consider a simple join of three relations, the natural join R(A,B) ⋈ S(B,C) ⋈ T(C,D). One way: cascade of two 2-way joins, each implemented by map-reduce. Fine, unless the 2-way joins produce large intermediate relations. Slide based on www.mmds.com

32. Another 3-Way Join Reduce processes use hash values of entire S(B,C) tuples as key. Choose a hash function h that maps B- and C-values to k buckets. There are k 2 Reduce processes, one for each (B-bucket, C-bucket) pair. Slide based on www.mmds.com

33. Job of the Reducers Each reducer gets, for certain B-values b and C-values c : 1.All tuples from R with B = b, 2.All tuples from T with C = c, and 3.The tuple S(b,c) if it exists. Thus it can create every tuple of the form (a, b, c, d) in the join. Slide based on www.mmds.com

34. Mapping for 3-Way Join uWe map each tuple S(b,c) to ((h(b), h(c)), (S, b, c)). uWe map each R(a,b) tuple to ((h(b), y), (R, a, b)) for all y = 1, 2,…,k. uWe map each T(c,d) tuple to ((x, h(c)), (T, c, d)) for all x = 1, 2,…,k. KeysValues Aside: even normal map-reduce allows inputs to map to several key-value pairs. Slide based on www.mmds.com

35. Assigning Tuples to Reducers h(b) = 0 1 2 3 h(c) = 0 1 2 3 S(b,c) where h(b)=1; h(c)=2 R(a,b), where h(b)=2 T(c,d), where h(c)=3 Slide based on www.mmds.com

36. DB = R(1,1) R(1,2) R(2,1) R(2,2) S(1,1) S(1,2) S(2,1) S(2,2) T(1,1) T(1,2) T(2,1) T(2,2)..etc R(1,1) R(2,1) S(1,1)T(1,1) T(1,2) R(1,1) R(2,1) S(1,2)T(2,1) T(2,2) R(1,2) R(2,2) S(2,1)T(1,1) T(1,2) R(1,2) R(2,2) S(2,2)T(2,1) T(2,2) Mapper R(1,1) ( 1,1,(R,1) ) ( 1,2,(R,1) ) Mapper S(1,2) ( 1,2,(S,1,2) )