mapreduce - duke universityexample4:matrixmultiplication 30 m n p 36 chapter 2. map-reduce and the...

Map-‐‑Reduce

Everything Data CompSci 290.01 Spring 2014

Announcements (Thu. Feb 27)

•  Homework #8 will be posted by noon tomorrow.

•  Project deadlines: – 2/25: Project team formation – 3/4: Project Proposal is due. – 3/4: 2 minute presentation in class

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2,161,530,000,000 searches in 2013

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131,000,000 pages mentioning Einstein

Size of the entire corpus??

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http://www.worldwidewebsize.com/

Size of the entire corpus??

Trend 1: Data centers 6

http://designtaxi.com/news/353991/Where-The-Internet-Lives-A-Glimpse-Inside-Google-s-Private-Data-Centers/

Trend 2: Multicore 7

Copyright © National Academy of Sciences. All rights reserved.

The Future of Computing Performance: Game Over or Next Level?

POWER IS NOW LIMITING GROWTH IN COMPUTING PERFORMANCE 91

expected performance. One might think that it should therefore be pos-sible to continue to scale performance by doubling the number of proces-sor cores. And, in fact, since the middle 1990s, some researchers have argued that chip multiprocessors (CMPs) can exploit capabilities of CMOS technology more effectively than single-processor chips.21 However, dur-ing the 1990s, the performance of single processors continued to scale at the rate of more than 50 percent per year, and power dissipation was still not a limiting factor, so those efforts did not receive wide attention. As single-processor performance scaling slowed down and the air-cooling power-dissipation limit became a major design constraint, researchers and industry shifted toward CMPs or multicore microprocessors.22

21 Kunle Olukotun, Basem A. Nayfeh, Lance Hammond, Ken Wilson, and Kunyung Chang, 1996, The case for a single-chip multiprocessor, Proceedings of 7th International Conference on Architectural Support for Programming Languages and Operating Systems, Cambridge, Mass., October 1-5, 1996, pp. 2-11.

22 Listed here are some of the references that document, describe, and analyze this shift: Michael Bedford Taylor, Walter Lee, Jason Miller, David Wentzlaff, Ian Bratt, Ben Greenwald, Henry Hoffmann, Paul Johnson, Jason Kim, James Psota, Arvind Saraf, Nathan Shnidman, Volker Strumpen, Matt Frank, Saman Amarasinghe, and Anant Agarwal, 2004, Evaluation of the raw microprocessor: An exposed-wire-delay architecture for ILP and streams, Pro-ceedings of the 31st Annual International Symposium on Computer Architecture, Munich,

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FIGURE 3.3 Microprocessor-clock frequency (MHz) over time (1985-2010).http://www.nap.edu/catalog.php?record_id=12980

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Moore’s Law: # transistors on integrated circuits doubles every 2 years

Need to think “parallel”

•  Data resides on different machines •  Split computation onto different machines/cores

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But … parallel programming is hard!

Low level code needs to deal with a lot of issues … •  Failures

– Loss of computation – Loss of data

•  Concurrency •  …

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Map-‐‑Reduce 10

Programming Model Distributed System

•  Simple model

•  Programmer only describes the logic

•  Works on commodity hardware

•  Scales to thousands of machines

•  Ship code to the data, rather than ship data to code

•  Hides all the hard systems problems from the programmer •  Machine failures •  Data placement •  …

+

Map Reduce Programming Model 11

map

reduce

f f f f f f f f

rows of dataset

g

Map-‐‑Reduce Programming Model 12

map!

!!, !! ! list! !!, !! !!reduce

!!!, list(!!) ! list! !!, !! !

!

map

reduce

f f f f f f f

g g

Example 1: Word Count

•  Input: A set of documents, each containing a list of words – Each document is a row – E.g., search queries, tweets, reviews, etc.

•  Output: A list of pairs <w, c> –  c is the number of times w appears across all documents.

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Word Count: Map

<docid, {list of words}> à {list of <word, 1>}

•  The mapper takes a document d and creates n key value pairs, one for each word in the document.

•  The output key is the word •  The output value is 1

–  (count of each appearance of a word)

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Word Count: Reduce <word, {list of counts}> à <word, sum(counts)>

•  The reducer aggregates the counts (in this case 1) associated with a specific word.

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Map-‐‑Reduce Implementation 16

Map Phase (per record computation)

Reduce Phase (global computation)

Shuffle

map!

!!, !! ! list! !!, !! !!reduce

!!!, list(!!) ! list! !!, !! !

!

Split




Shuffle

Split

Split phase partitions the data across different mappers (… think different machines)




Shuffle

Split

Each mapper executes user defined map code on the partitions in parallel




Shuffle

Split

Data is shuffled such that there is one reducer per output key (… again think different machines)




Shuffle

Split

Each reducer executes the user defined reduce code in parallel.

Map Reduce Implementation

•  After every map and reduce phase, data is wriien onto disk –  If machines fail during the reduce phase, then no need to rerun the mappers.

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Writing to disk is slow. Should minimize number of map-‐‑reduce phases.

Mappers, Reducers and Workers

•  Physical machines are called workers •  Multiple mappers and reducers can run on the same worker.

•  More workers implies … … more parallelism (faster computation) … … but more (communication) overhead …

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Map Reduce Implementation

•  All reducers start only after all the mappers complete.

•  Straggler: A mapper or reducer that takes a long time

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Back to Word Count

•  Map: <docid, {list of words}> à {list of <word, 1>}

•  Reduce: <word, {list of counts}> à <word, sum(counts)>

•  Number of records output by the map phase equals the number of words across all documents.

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Map-‐‑Combine-‐‑Reduce

•  Combiner is a mini-‐‑reducer within each mapper. – Helps when the reduce function is commutative and associative.

•  Aggregation within each mapper reduces the communication cost.

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Word Count … with combiner •  Map:

<docid, {list of words}> à {list of <word, 1>}

•  Combine: <word, {list of counts}> à <word, sum(counts)>

•  Reduce: <word, {list of counts}> à <word, sum(counts)>

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Mapper

Reducer

Word Count … in python 27

One of the many MapReduce libraries for python

Example 2: K most frequent words

•  Need multiple Map-‐‑Reduce steps

•  Map: <docid, {list of words}> à {list of <word, 1>}

•  Reduce: <word, {list of counts}> à <_ , (word, sum(counts))>

•  Reduce: <_ , {list of (word, count) pairs}> à <_ , {list of words with k most frequent counts}>

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Example 3: Distributed Grep

•  Input: String •  Output: {list of lines that match the string}

•  Map: <lineid, line> à <lineid, line> // if line matches string

•  Reduce: // do nothing

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Example 4: Matrix Multiplication 30

M N P

36 CHAPTER 2. MAP-REDUCE AND THE NEW SOFTWARE STACK

the Reduce function applies each of them to the list of values associated witha given key and produces a tuple consisting of the key, including componentsfor all grouping attributes if there is more than one, followed by the results ofeach of the aggregations.

2.3.9 Matrix Multiplication

If M is a matrix with element mij in row i and column j, and N is a matrixwith element njk in row j and column k, then the product P = MN is thematrix P with element pik in row i and column k, where

pik =!

j

mijnjk

It is required that the number of columns of M equals the number of rows ofN , so the sum over j makes sense.

We can think of a matrix as a relation with three attributes: the row number,the column number, and the value in that row and column. Thus, we could viewmatrix M as a relation M(I, J, V ), with tuples (i, j, mij), and we could viewmatrix N as a relation N(J, K, W ), with tuples (j, k, njk). As large matrices areoften sparse (mostly 0’s), and since we can omit the tuples for matrix elementsthat are 0, this relational representation is often a very good one for a largematrix. However, it is possible that i, j, and k are implicit in the position of amatrix element in the file that represents it, rather than written explicitly withthe element itself. In that case, the Map function will have to be designed toconstruct the I, J , and K components of tuples from the position of the data.

The product MN is almost a natural join followed by grouping and ag-gregation. That is, the natural join of M(I, J, V ) and N(J, K, W ), havingonly attribute J in common, would produce tuples (i, j, k, v, w) from each tuple(i, j, v) in M and tuple (j, k, w) in N . This five-component tuple represents thepair of matrix elements (mij , njk). What we want instead is the product ofthese elements, that is, the four-component tuple (i, j, k, v × w), because thatrepresents the product mijnjk. Once we have this relation as the result of onemap-reduce operation, we can perform grouping and aggregation, with I andK as the grouping attributes and the sum of V × W as the aggregation. Thatis, we can implement matrix multiplication as the cascade of two map-reduceoperations, as follows. First:

The Map Function: For each matrix element mij , produce the key value pair"

j, (M, i, mij)#

. Likewise, for each matrix element njk, produce the key valuepair

"

j, (N, k, njk)#

. Note that M and N in the values are not the matricesthemselves. Rather they are names of the matrices or (as we mentioned for thesimilar Map function used for natural join) better, a bit indicating whether theelement comes from M or N .

The Reduce Function: For each key j, examine its list of associated values.For each value that comes from M , say (M, i, mij)

#

, and each value that comes

x =

Matrix Multiplication •  Assume the input format is <matrix id, row, col, entry>

•  E.g.: <M, i, j, mij>

•  Map: <_ , (M, i, j, mij)> à <(i,k), (M, i, mij)> … for all k

<_ , (N, j, k, njk)> à <(i,k), (N, k, njk)> … for all i •  Reduce: <(i,k), {(M, i, j, mij), (N, j, k, njk) …}> à { <(i,k), Σj mijnjk>}

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Example 5: Join two tables

•  Input: file1 and file2, with schema <key, value> •  Output: keys appearing in both files.

•  Map: <_ , (file1, key, value)> à (key, file1) <_ , (file2, key, value)> à (key, file2)

•  Reduce: <key , {list of fileids}> à <_, key> // if list contains both file1 and file2.

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Map-‐‑side Join

•  Suppose file2 is very small …

•  Map: <_ , (file1, key, value, {keys in file2})> à (_ , key) // If key is also in file2

•  Reduce: // do nothing <_ , {list of keys}> à <_ , {list of keys}>

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Send contents of file2 to all the mappers

Example 5: Join 3 tables

•  Input: 3 Tables – User (id:int, age:int) – Page (url:varchar, category:varchar) – Log (userid: int, url:varchar)

•  Output: Ages of users and types of urls they clicked.

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Multiway Join •  Join( Page, Join (User , Log)) •  Map:

<_ , (User, id, age)> à (id, (User, key, value)) <_ , (Log, userid, url)> à (userid, (Log, userid, url))

•  Reduce: <id, {list of records}> à <_, {records from User} x {records from Log}> // if list contains records both from User and Log.

•  Map: <_ , (User, Log, id, age, userid, url)> à (url, (User, Log, id, age, userid, url)) <_ , (Page, url, category)> à (url, (Page, url, category))

•  Reduce: <url, {list of records}> à <_, {records from User x Log} x {records from Page}> // if list contains records both from User x Log and Page.

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Summary

•  Map-‐‑reduce is a programming model + distributed system implementation that make parallel programming easy. – User does not need to worry about systems issues.

•  Computation is a series of Map and Reduce jobs. – Parallelism is achieved within each Map and Reduce phase.

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mapreduce - duke universityexample4:matrixmultiplication 30 m n p 36 chapter 2. map-reduce and the...

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