MapReduce Algorithms

Algorithms for MapReduce
• Sorting
• Searching
• Indexing
• Classification
• Joining
• TF-IDF
© 2009 Cloudera, Inc.
MapReduce Jobs
• Tend to be very short, code-wise
– IdentityReducer is very common
• “Utility” jobs can be composed
• Represent a data flow, more so than a
procedure

Sort: Inputs
• A set of files, one value per line.
• Mapper key is file name, line number
• Mapper value is the contents of the line

Sort Algorithm
• Takes advantage of reducer properties:
(key, value) pairs are processed in order
by key; reducers are themselves ordered
• Mapper: Identity function for value
(k, v)
(v, _)
• Reducer: Identity function (k’, _) -> (k’, “”)

Sort: The Trick
• (key, value) pairs from mappers are sent to a
particular reducer based on hash(key)
• Must pick the hash function for your data such
that k
1 < k2 => hash(k1) < hash(k2)

 
 

Final Thoughts on Sort
• Used as a test of Hadoop’s raw speed
• Essentially “IO drag race”
• Highlights utility of GFS

Search: Inputs
• A set of files containing lines of text
• A search pattern to find
• Mapper key is file name, line number
• Mapper value is the contents of the line
• Search pattern sent as special parameter

Search Algorithm
• Mapper:
– Given (filename, some text) and “pattern”, if
“text” matches “pattern” output (filename, _)
• Reducer:
– Identity function
.
Search: An Optimization
• Once a file is found to be interesting, we
only need to mark it that way once
• Use Combiner function to fold redundant
(filename, _) pairs into a single one
– Reduces network I/O
© 2009 Cloudera, Inc.
Indexing: Inputs
• A set of files containing lines of text
• Mapper key is file name, line number
• Mapper value is the contents of the line

Inverted Index Algorithm
• Mapper: For each word in (file, words),
map to (word, file)
• Reducer: Identity function

Index: MapReduce
map(pageName, pageText):
foreach word w in pageText:
emitIntermediate(w, pageName);
done
reduce(word, values):
foreach pageName in values:
AddToOutputList(pageName);
done
emitFinal(FormattedPageListForWord);
© 2009 Cloudera, Inc.
Index: Data Flow
.
An Aside: Word Count
• Word count was described in module I
• Mapper for Word Count is (word, 1) for
each word in input line
– Strikingly similar to inverted index
– Common theme: reuse/modify existing
mappers
.
Bayesian Classification
• Files containing classification instances
are sent to mappers
• Map (filename, instance)
(instance,
class)
• Identity Reducer

Bayesian Classification
• Existing toolsets exist to perform Bayes
classification on instance
– E.g., WEKA, already in Java!
• Another example of discarding input key

Joining
• Common problem: Have two data types,
one includes references to elements of the
other; would like to incorporate data by
value, not by reference
• Solution: MapReduce Join Pass

Join Mapper
• Read in all values of joiner, joinee classes
• Emit to reducer based on primary key of
joinee (i.e., the reference in the joiner, or
the joinee’s identity)
© 2009 Cloudera, Inc.
Join Reducer
• Joinee objects are emitted as-is
• Joiner objects have additional fields
populated by Joinee which comes to the
same reducer as them.
– Must do a secondary sort in the reducer to
read the joinee before emitting any objects
which join on to it

TF-IDF
• Term Frequency – Inverse Document
Frequency
– Relevant to text processing
– Common web analysis algorithm
© 2009 Cloudera, Inc.
The Algorithm, Formally
•| D | : total number of documents in the corpus
• : number of documents where the term t
i appears (that is ).

Information We Need
• Number of times term X appears in a
given document
• Number of terms in each document
• Number of documents X appears in
• Total number of documents
© 2009 Cloudera, Inc.
Job 1: Word Frequency in Doc
• Mapper
– Input: (docname, contents)
– Output: ((word, docname), 1)
• Reducer
– Sums counts for word in document
– Outputs ((word, docname), n)
• Combiner is same as Reducer

Job 2: Word Counts For Docs
• Mapper
– Input: ((word, docname), n)
– Output: (docname, (word, n))
• Reducer
– Sums frequency of individual n’s in same doc
– Feeds original data through
– Outputs ((word, docname), (n, N))
Job 3: Word Frequency In Corpus
• Mapper
– Input: ((word, docname), (n, N))
– Output: (word, (docname, n, N, 1))
• Reducer
– Sums counts for word in corpus
– Outputs ((word, docname), (n, N, m))
© 2009 Cloudera, Inc.
Job 4: Calculate TF-IDF
• Mapper
– Input: ((word, docname), (n, N, m))
– Assume D is known (or, easy MR to find it)
– Output ((word, docname), TF*IDF)
• Reducer
– Just the identity function

Working At Scale
• Buffering (doc, n, N) counts while
summing 1’s into m may not fit in memory
– How many documents does the word “the”
occur in?
• Possible solutions
– Ignore very-high-frequency words
– Write out intermediate data to a file
– Use another MR pass

Final Thoughts on TF-IDF
• Several small jobs add up to full algorithm
• Lots of code reuse possible
– Stock classes exist for aggregation, identity
• Jobs 3 and 4 can really be done at once in
same reducer, saving a write/read cycle
• Very easy to handle medium-large scale,
but must take care to ensure flat memory
usage for largest scale

Conclusions
• Lots of high level algorithms
• Lots of deep connections to low-level
systems