MapReduce: Simplified Data Processing on Large Clusters

MapReduce is a programming model and an associated implementation for processing and generating large data sets.

map function: processes a key/value pair to generate a set of intermediate key/value pairs
reduce function: merges all intermediate values associated with the same intermediate key

partitioning the input data, scheduling the program’s execution across a set of machines, handling machine failures, and managing the required inter-machine communication

1 Introduction

The issues of how to parallelize the computation, distribute the data, and handle failures conspire to obscure the original simple computation with large amounts of complex code to deal with these issues.

new abstraction:

map operation to each logical “record” in our input in order to compute a set of intermediate key/value pairs
reduce operation to all the values that shared the same key, in order to combine the derived data appropriately

(inspired by the map and reduce primitives present in Lisp and many other functional languages)

2 Programming Model

input: key/value pairs

output: key/value pairs

Map: written by the user, take an input pair and produces a set of intermediate key/value pairs. The MapReduce library groups together all intermediate values associated with the same intermediate key I and passes them to the Reduce function.
Reduce: also written by the user, accepts an intermediate key I and a set of values for that key. It merges together these values to form a possibly smaller set of values. Typically just zero or one output value is produced per Reduce invocation. The intermediate values are supplied to the user’s reduce function via an iterator. (to handle lists of values that are too large to fit in memory)

2.1 Example

Counting the number of occurrences of each word in a large collection of documents. The user would write code similar to the following pseudo-code:

map(String key, String value):
  // key: document name
  // value: document contents
  for each word w in value:
    EmitIntermediate(w, "1");

reduce(String key, Iterator values):
  // key: a word
  // values: a list of counts
  int result = 0;
  for each v in values:
    result += ParseInt(v);
  Emit(AsString(result));

In addition, the user writes code to fill in a mapreduce specification object with the names of the input and output files, and optional tuning parameters. The user then invokes the MapReduce function, passing it the specification object.

2.2 Types

Conceptually the map and reduce functions supplied by the user have associated types:

map     (k1, v1)       -> list(k2, v2)
reduce  (k2, list(v2)) -> list(v2)

The input keys and values are drawn from a different domain than the output keys and values. The intermediate keys and values are from the same domain as the output keys and values.

2.3 More Examples

Distributed Grep
The map function emits a line if it matches a supplied pattern.
The reduce function is an identity function that just copies the supplied intermediate data to the output.
Count of URL Access Frequency
The map function processes logs of web page requests and outputs <URL, 1>.
The reduce function adds together all values for the same URL and emits a <URL, total count> pair.
Reverse Web-Link Graph
The map function outputs <target, source> pairs for each link to a target URL found in a page named source.
The reduce function concatenates the list of all source URLs associated with a given target URL and emits the pair: <target, list(source)>.
Term-Vector per Host
A term vector summarizes the most important words that occur in a document or a set of documents as a list of $⟨word, frequency⟩$ pairs.
The map function emits a <hostname, term vector> pair for each input document (where the hostname is extracted from the URL of the document).
The reduce function is passed all per-document term vectors for a given host. It adds these term vectors together, throwing away infrequent terms, and then emits a final <hostname, term vector> pair.
Inverted Index
The map function parses each document, and emits a sequence of <word, document ID> pairs.
The reduce function accepts all pairs for a given word, sorts the corresponding document IDs and emits a <word, list(document ID)> pair.
The set of all output pairs forms a simple inverted index. It is easy to augment this computation to keep track of word position.
Distributed Sort
The map function extracts the key from each record, and emits a <key, record> pair.
The reduce function emits all pairs unchanged.
This computation depends on the partitioning facilities described in Section 4.1 and the ordering properties described in Section 4.2.

3 Implementation

This section describes an implementation targeted to the computing environment: large clusters of commodity PCs connected together with switched Ethernet.

A cluster consists of hundreds of thousands of machines, and therefore machine failures are common.
A distributed file system (GFS) is used to manage the data stored on the disks attached directly to individual machines. The file system uses replication to provide availability and reliability on top of unreliable hardware.
Users submit jobs to a scheduling system. Each job consists of a set of tasks, and is mapped by the scheduler to a set of available machines within a cluster.

3.1 Execution Overview

The Map invocations are distributed across multiple machines by automatically partitioning the input data into a set of M splits. The input splits can be processed in parallel by different machines.

Reduce invocations are distributed by partitioning the intermediate key space into R pieces using a partitioning function (e.g., $hash(key) \mod R$ ). The number of partitions (R) and the partitioning function are specified by the user.

When the user program calls the MapReduce function, the following sequence of actions occurs:

The MapReduce library in the user program first splits the input files into M pieces of typically 16 megabytes to 64 megabytes (MB) per piece (controllable by the user via an optional parameter). It then starts up many copies of the program on a cluster of machines.
One of the copies of the program is special — the master. The rest are workers that are assigned work by the master. There are M map tasks and R reduce tasks to assign. The master picks idle workers and assigns each one a map task or a reduce task.
A worker who is assigned a map task reads the contents of the corresponding input split. It parses key/value pairs out of the input data and passes each pair to the user-defined Map function. The intermediate key/value pairs produced by the Map function are buffered in memory.
Periodically, the buffered pairs are written to local disk, partitioned into R regions by the partitioning function. The locations of these buffered pairs on the local disk are passed back to the master, who is responsible for forwarding these locations to the reduce workers.
When a reduce worker is notified by the master about these locations, it uses remote procedure calls to read the buffered data from the local disks of the map workers. When a reduce worker has read all intermediate data, it sorts it by the intermediate keys so that all occurrences of the same key are grouped together. The sorting is needed because typically many different keys map to the same reduce task. If the amount of intermediate data is too large to fit in memory, an external sort is used.
The reduce worker iterates over the sorted intermediate data and for each unique intermediate key encountered, it passes the key and the corresponding set of intermediate values to the user’s Reduce function. The output of the Reduce function is appended to a final output file for this reduce partition.
When all map tasks and reduce tasks have been completed, the master wakes up the user program. At this point, the MapReduce call in the user program returns back to the user code.

After successful completion, the output of the mapreduce execution is available in the R output files (one per reduce task, with file names as specified by the user). Typically, users do not need to combine these R output files into one file — they often pass these files as input to another MapReduce call, or use them from another distributed application that is able to deal with input that is partitioned into multiple files.

3.2 Master Data Structures

For each map task and reduce task, the master stores the state (idle, in-progress, or completed), and the identity of the worker machine (for non-idle tasks).

The master is the conduit through which the location of intermediate file regions is propagated from map tasks to reduce tasks. Therefore, for each completed map task, the master stores the locations and sizes of the R intermediate file regions produced by the map task. Updates to this location and size information are received as map tasks are completed. The information is pushed incrementally to workers that have in-progress reduce tasks.

3.3 Fault Tolerance

Worker Failure

The master pings every worker periodically. If no response is received from a worker in a certain amount of time, the master marks the worker as failed.

Completed map tasks are re-executed on a failure because their output is stored on the local disk(s) of the failed machine and is therefore inaccessible. Completed reduce tasks do not need to be re-executed since their output is stored in a global file system.

When a map task is executed first by worker A and then later executed by worker B (because A failed), all workers executing reduce tasks are notified of the re-execution. Any reduce tasks that has not already read the data from worker A will read the data from worker B.

Master Failure

The master writes periodic checkpoints of the master data structures described above. If the master task dies, a new copy can be started from the last checkpointed state.

(However, given that there is only a single master, its failure is unlikely; therefore our current implementation aborts the MapReduce computation if the master fails. Clients can check for this condition and retry the MapReduce operation if they desire.)

Semantics in the Presence of Failures

When the user-supplied map and reduce operators are deterministic functions of their input values, our distributed implementation produces the same output as would have been produced by a non-faulting sequential execution of the entire program.

We rely on atomic commits of map and reduce task outputs to achieve this property.

Each in-progress task writes its output to private temporary files. A reduce task produces one such file, and a map task produces R such files (one per reduce task).

When a map task completes, the worker sends a message to the master and includes the names of the R temporary files in the message. If the master receives a completion message for an already completed map task, it ignores the message. Otherwise, it records the name of R files in a master data structure.
When a reduce task completes, the reduce worker atomically renames its temporary output file to the final output file. If the same reduce task is executed on multiple machines, multiple rename calls will be executed for the same final output file. We rely on the atomic rename operation provided by the underlying file system to guarantee that the final file system state contains just the data produced by one execution of the reduce task.

When the map and/or reduce operators are non-deterministic, we provide weaker but still reasonable semantics. In the presence of non-deterministic operators, the output of a particular reduce task $R_1$ is equivalent to the output for $R_1$ produced by a sequential execution of the non-deterministic program. However, the output for a different reduce task $R_2$ may correspond to the output for $R_2$ produced by a different sequential execution of the non-deterministic program.

Consider map task $M$ and reduce tasks $R_1$ and $R_2$ . Let $e(R_i)$ be the execution of $R_i$ that committed (there is exactly one such execution). The weaker semantics arise because $e(R_1)$ may have read the output produced by one execution of $M$ and $e(R_2)$ may have read the output produced by a different execution of $M$ .

3.4 Locality

We conserve network bandwidth by taking advantage of the fact that the input data (managed by GFS) is stored on the local disks of the machines that make up our cluster.

GFS divides each file into 64 MB blocks, and stores several copies of each block (typically 3 copies) on different machines. The MapReduce master takes the location information of the input files into account and attempts to schedule a map task on a machine that contains a replica of the corresponding input data. Failing that, it attempts to schedule a map task near a replica of that task’s input data (e.g., on a worker machine that is on the same network switch as the machine containing the data).

3.5 Task Granularity

We subdivide the map phase into M pieces and the reduce phase into R pieces. Ideally, M and R should be much larger than the number of worker machines.

improve dynamic load balancing
speed up recovery when a worker fails: completed map tasks can be spread out across all the other worker machines

Practical bounds:

The master must take $O(M+R)$ scheduling decisions and keeps $O(M*R)$ state in memory.