1. Google’s Map Reduce

2. Commodity Clusters Web data sets can be very large – Tens to hundreds of terabytes Standard architecture emerging: – Cluster of commodity Linux nodes – Gigabit Ethernet interconnect How to organize computations on this architecture?

3. Cluster Architecture Mem Disk CPU Mem Disk CPU … Switch Each rack contains 16-64 nodes Mem Disk CPU Mem Disk CPU … Switch 1 Gbps between any pair of nodes in a rack 2-10 Gbps backbone between racks

4. Map Reduce Map-reduce is a high-level programming system that allows database processes to be written simply. The user writes code for two functions, map and reduce. A master controller divides the input data into chunks, and assigns different processors to execute the map function on each chunk. Other processors, perhaps the same ones, are then assigned to perform the reduce function on pieces of the output from the map function.

5. The Map Function Each map process is given a chunk of input data Input is thought of as a set of key-value records. Output is a set of key-value pairs. – Of course not the same as the key-value pairs in the input. – The "keys" are not true keys in the database sense. That is, there can be many pairs with the same key value.

6. Map Example Constructing an Inverted Index Map Function Input is a set of (i,d) pairs – i is document ID – d is corresponding document. The map function scans d and for each word w it finds, it emits the pair (w, i). – Notice that in the output, the word is the key and the document ID is the associated value. Output is a list of word-ID pairs. – Not necessary to catch duplicate words in the document; this can be done later, at the reduce phase.

7. The system will take care the key-value pairs with the same key end up in the same reduce instance.

8. The Reduce Function Input to reduce is a set of key-value pairs that were output by map instances. – All the the key-value pairs with the same key end up in the same reduce instance. – A set (k,v 1 ), …, (k,v n ) of key-value pairs can be considered as (k,[v 1,…,v n ]). Reduce function combines the list of values associated with a given key k.

9. Reduce Example Constructing an Inverted Index Reduce Function The intermediate result consists of pairs of the form (w, [i 1, i 2,…,i n ]), – where the i's are a list of document ID's, one for each occurrence of word w. The reduce function takes a list of ID's, eliminates duplicates, and sorts the list of unique ID's.

10. Parallelism This organization of the computation makes excellent use of whatever parallelism is available. The map function works on a single document, so we could have as many processes and processors as there are documents in the database. The reduce function works on a single word, so we could have as many processes and processors as there are words in the database. Of course, it is unlikely that we would use so many processors in practice.

11. Another Example – Word Count Construct a word count. For each word w that appears at least once in our database of documents, output pair (w, c), where c is the number of times w appears among all the documents. The map function Input is a document. Goes through the document, and each time it encounters another word w, it emits the pair (w, 1). Intermediate result is a list of pairs (w 1,1), (w 2,1),…. The reduce function Input is a pair (w, [1, 1,...,1]), with a 1 for each occurrence of word w. Sums the 1's, producing the count. Output is word-count pairs (w,c).

12. What about Joins? R(A, B)  S(B, C) The map function Input is key-value pairs (X, t), – X is either R or S, – t is a tuple of the relation named by X. Output is a single pair (b, (R, a)) or (b, (S, c)) depending on X – b is the B-value of t. – b is the B-value of t (if X=R). – c is the C-value of t (if X=C). The reduce function Input is a pair (b, [(R,a), (S,c), …]). Extracts all the A-values associated with R and all C-values associated with S. These are paired in all possible ways, with the b in the middle to form a tuple of the result.

13. Reading Jeffrey Dean and Sanjay Ghemawat, MapReduce: Simplified Data Processing on Large Clusters http://labs.google.com/papers/mapreduce.html Hadoop (Apache) – Open Source implementation of MapReduce http://hadoop.apache.org/core