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{{Short description|Algorithm which can do multiple operations in a given time}}
{{More citations needed|date=November 2012}}
In [[computer science]], a '''parallel algorithm''', as opposed to a traditional [[serial algorithm]], is an [[algorithm]] which can do multiple operations in a given time. It has been a tradition of [[computer science]] to describe serial algorithms in [[abstract machine]] models, often the one known as [[random-access machine]]. Similarly, many computer science researchers have used a so-called [[parallel random-access machine]] (PRAM) as a parallel abstract machine (shared-memory).<ref>{{cite web |title=Parallel Algorithms |first1=Guy E. |last1=Blelloch |first2=Bruce M. |last2=Maggs |publisher=School of Computer Science, [[Carnegie Mellon University]] |location=USA |access-date=2015-07-27 |url=https://www.cs.cmu.edu/~guyb/papers/BM04.pdf}}</ref><ref>{{cite web |title=Thinking in Parallel: Some Basic Data-Parallel Algorithms and Techniques, 104 pages |first=Uzi |last=Vishkin |publisher=Class notes of courses on parallel algorithms taught since 1992 at the University of Maryland, College Park, Tel Aviv University and the Technion |date=2009 |url=http://users.umiacs.umd.edu/~vishkin/PUBLICATIONS/classnotes.pdf}}</ref>

Many parallel algorithms are executed [[concurrent computing|concurrently]] – though in general [[concurrent algorithm]]s are a distinct concept – and thus these concepts are often conflated, with which aspect of an algorithm is parallel and which is concurrent not being clearly distinguished. Further, non-parallel, non-concurrent algorithms are often referred to as "[[sequential algorithm]]s", by contrast with concurrent algorithms.

==Parallelizability==
{{see also|Analysis of parallel algorithms}}
Algorithms vary significantly in how parallelizable they are, ranging from easily parallelizable to completely unparallelizable. Further, a given problem may accommodate different algorithms, which may be more or less parallelizable.

Some problems are easy to divide up into pieces in this way – these are called ''[[embarrassingly parallel]] problems.'' Examples include many algorithms to solve [[Rubik's Cube]]s and find values which result in a given [[associative array|hash]].{{citation needed|date=December 2019}}

Some problems cannot be split up into parallel portions, as they require the results from a preceding step to effectively carry on with the next step – these are called '''{{visible anchor|inherently serial problem}}s'''. Examples include iterative [[numerical analysis|numerical methods]], such as [[Newton's method]], iterative solutions to the [[three-body problem]], and most of the available algorithms to compute [[pi]] (π).{{citation needed|date=August 2019}} Some sequential algorithms can be converted into parallel algorithms using [[automatic parallelization]].<ref name="MXian1997">{{cite book |author1=Megson G M|author2=Chen Xian|title=Automatic Parallelization For A Class Of Regular Computations|url=https://books.google.com/books?id=1wHtCgAAQBAJ&q=%22parallel+algorithm%22|date=4 January 1997|publisher=World Scientific|isbn=978-981-4498-41-8}}</ref>

In many cases developing an effective parallel algorithm to solve a task requires developing new ideas and methods not needed in the design of a sequential algorithm to solve the same problem. Examples of such cases include the practically important problems of searching for a target element in a data structure and the evaluation of an algebraic expression.<ref>{{Cite book |last=Kurgalin |first=Sergei |title=The discrete math workbook: a companion manual using Python |last2=Borzunov |first2=Sergei |date=2020 |publisher=Springer Naturel |isbn=978-3-030-42220-2 |edition=2nd |series=Texts in Computer Science |location=Cham, Switzerland}}</ref>

==Motivation==
Parallel algorithms on individual devices have become more common since the early 2000s because of substantial improvements in [[multiprocessing]] systems and the rise of [[multi-core]] processors. Up until the end of 2004, single-core processor performance rapidly increased via [[frequency scaling]], and thus it was easier to construct a computer with a single fast core than one with many slower cores with the same [[throughput]], so multicore systems were of more limited use. Since 2004 however, frequency scaling hit a wall, and thus multicore systems have become more widespread, making parallel algorithms of more general use.

==Issues==

===Communication===
The cost or complexity of serial algorithms is estimated in terms of the space (memory) and time (processor cycles) that they take. Parallel algorithms need to optimize one more resource, the communication between different processors. There are two ways parallel processors communicate, shared memory or message passing.

[[Shared memory]] processing needs additional [[lock (computer science)|locking]] for the data, imposes the overhead of additional processor and bus cycles, and also serializes some portion of the algorithm.

[[Message passing]] processing uses channels and message boxes but this communication adds transfer overhead on the bus, additional memory need for queues and message boxes and latency in the messages. Designs of parallel processors use special [[bus (computing)|buses]] like [[crossbar switch|crossbar]] so that the communication overhead will be small but it is the parallel algorithm that decides the volume of the traffic.

If the communication overhead of additional processors outweighs the benefit of adding another processor, one encounters [[parallel slowdown]].

===Load balancing===
{{main|Load balancing (computing)}}
Another problem with parallel algorithms is ensuring that they are suitably [[load balancing (computing)|load balanced]], by ensuring that ''load'' (overall work) is balanced, rather than input size being balanced. For example, checking all numbers from one to a hundred thousand for primality is easy to split among processors; however, if the numbers are simply divided out evenly (1–1,000, 1,001–2,000, etc.), the amount of work will be unbalanced, as smaller numbers are easier to process by this algorithm (easier to test for primality), and thus some processors will get more work to do than the others, which will sit idle until the loaded processors complete.

==Distributed algorithms==
{{main|Distributed algorithm}}
{{expand section|date=February 2014}}
A subtype of parallel algorithms, ''[[distributed algorithm]]s'', are algorithms designed to work in [[cluster computing]] and [[distributed computing]] environments, where additional concerns beyond the scope of "classical" parallel algorithms need to be addressed.

Distributed algorithms are intended to run on a network of interconnected computers that communicate through shared memory or message passing. Unlike traditional parallel algorithms, they must operate under additional constraints such as limited local knowledge, communication delays, the lack of a global state, and the possibility of node failures.

The focus of distributed algorithms is on coordination problems that arise in distributed systems, including [[leader election]], [[mutual exclusion]], and [[consensus (computer science)]]. These problems are studied under different system models with varying assumptions, such as whether the system is synchronous or asynchronous and if there are failures, such as crash failures or [[Byzantine fault|Byzantine failures]].<ref>Hagit Attiya and Jennifer Welch. ''Distributed Computing: Fundamentals, Simulations, and Advanced Topics''. 2nd ed., Wiley, 2004.</ref>

Distributed algorithms have many practical applications in distributed databases, fault-tolerance systems, and large-scale networked applications.

==See also==
* [[Multiple-agent system]] (MAS)
* [[Parallel algorithms for matrix multiplication]]
* [[Parallel algorithms for minimum spanning trees]]
* [[Parallel computing]]
* [[Parareal]]

==References==
{{Reflist}}

==External links==
*[https://www.mcs.anl.gov/~itf/dbpp/ Designing and Building Parallel Programs], US Argonne National Laboratory

{{Parallel computing}}
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[[Category:Parallel computing]]
[[Category:Concurrent algorithms]]
[[Category:Distributed algorithms]]