# Parallel algorithm

 related topics {system, computer, user} {math, number, function}

In computer science, a parallel algorithm or concurrent algorithm, as opposed to a traditional sequential (or serial) algorithm, is an algorithm which can be executed a piece at a time on many different processing devices, and then put back together again at the end to get the correct result.

Some algorithms are easy to divide up into pieces like this. For example, splitting up the job of checking all of the numbers from one to a hundred thousand to see which are primes could be done by assigning a subset of the numbers to each available processor, and then putting the list of positive results back together.

Most of the available algorithms to compute pi (π), on the other hand, cannot be easily split up into parallel portions. They require the results from a preceding step to effectively carry on with the next step. Such problems are called inherently serial problems. Iterative numerical methods, such as Newton's method or the three-body problem, are also algorithms which are inherently serial. Some problems are very difficult to parallelize, although they are recursive. One such example is the depth-first search of graphs.

Parallel algorithms are valuable because of substantial improvements in multiprocessing systems and the rise of multi-core processors. In general, it is easier to construct a computer with a single fast processor than one with many slow processors with the same throughput. But processor speed is increased primarily by shrinking the circuitry, and modern processors are pushing physical size and heat limits. These twin barriers have flipped the equation, making multiprocessing practical even for small systems.

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 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 buses like crossbar so that the communication overhead will be small but it is the parallel algorithm that decides the volume of the traffic.

Another problem with parallel algorithms is ensuring that they are suitably load balanced. For example, checking all numbers from one to a hundred thousand for primality is easy to split amongst processors; however, some processors will get more work to do than the others, which will sit idle until the loaded processors complete.

A subtype of parallel algorithms, distributed algorithms 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.