Bulk synchronous parallel

The bulk synchronous parallel (BSP) abstract computer is a bridging model for designing parallel algorithms. It is similar to the parallel random access machine (PRAM) model, but unlike PRAM, BSP does not take communication and synchronization for granted. In fact, quantifying the requisite synchronization and communication is an important part of analyzing a BSP algorithm.
History.
The BSP model was developed by Leslie Valiant of Harvard University during the 1980s. The definitive article was published in 1990.
Between 1990 and 1992, Leslie Valiant and Bill McColl of Oxford University worked on ideas for a distributed memory BSP programming model, in Princeton and at Harvard. Between 1992 and 1997, McColl led a large research team at Oxford that developed various BSP programming libraries, languages and tools, and also numerous massively parallel BSP algorithms. With interest and momentum growing, McColl then led a group from Oxford, Harvard, Florida, Princeton, Bell Labs, Columbia and Utrecht that developed and published the BSPlib Standard for BSP programming in 1996.
Valiant developed an extension to the BSP model in the 2000s, leading to the publication of the Multi-BSP model in 2011.
In 2017, McColl developed a major new extension of the BSP model that provides fault tolerance and tail tolerance for large-scale parallel computations in AI, Analytics and high-performance computing (HPC).
The BSP model.
Overview.
A BSP computer consists of:
This is commonly interpreted as a set of processors that may follow different threads of computation, with each processor equipped with fast local memory and interconnected by a communication network.
BSP algorithms rely heavily on the third feature; a computation proceeds in a series of global "supersteps", which consists of three components:
The computation and communication actions do not have to be ordered in time. Communication typically takes the form of the one-sided "PUT" and "GET" remote direct memory access (RDMA) calls, rather than paired two-sided "send" and "receive" message-passing calls.
The barrier synchronization concludes the superstep—it ensures that all one-sided communications are properly concluded. Systems based on two-sided communication include this synchronisation cost implicitly for every message sent. The method for barrier synchronisation relies on the hardware facility of the BSP computer. In Valiant's original paper, this facility periodically checks if the end of the current superstep is reached globally. The period of this check is denoted by formula_1. 
The BSP model is also well-suited for automatic memory management for distributed-memory computing through over-decomposition of the problem and oversubscription of the processors. The computation is divided into more logical processes than there are physical processors, and processes are randomly assigned to processors. This strategy can be shown statistically to lead to almost perfect load balancing, both of work and communication.
Communication.
In many parallel programming systems, communications are considered at the level of individual actions such as sending and receiving a message or memory-to-memory transfer. This is difficult to work with since there are many simultaneous communication actions in a parallel program, and their interactions are typically complex. In particular, it is difficult to say much about the time any single communication action will take to complete.
The BSP model considers communication actions "en masse". This has the effect that an upper bound on the time taken to communicate a set of data can be given. BSP considers all communication actions of a superstep as one unit, and assumes all individual messages sent as part of this unit have a fixed size.
The maximum number of incoming or outgoing messages for a superstep is denoted by formula_2. The ability of a communication network to deliver data is captured by a parameter formula_3, defined such that it takes time formula_4 for a processor to deliver formula_2 messages of size 1.
A message of length formula_6 obviously takes longer to send than a message of size 1. However, the BSP model does not make a distinction between a message length of formula_6 or formula_6 messages of length 1. In either case the cost is said to be formula_9.
The parameter formula_3 depends on the following:
In practice, formula_3 is determined empirically for each parallel computer. Note that formula_3 is not the normalised single-word delivery time, but the single-word delivery time under continuous traffic conditions.
Barriers.
The one-sided communication of the BSP model requires barrier synchronization. 
Barriers are potentially costly, but avoid the possibility of deadlock or livelock, since barriers cannot create circular data dependencies. Tools to detect them and deal with them are unnecessary. Barriers also permit novel forms of fault tolerance.
The cost of barrier synchronization is influenced by a couple of issues:
The cost of a barrier synchronization is denoted by formula_13. Note that formula_14 if the synchronisation mechanism of the BSP computer is as suggested by Valiant. 
In practice, a value of formula_13 is determined empirically.
On large computers, barriers are expensive, and this is increasingly so on large scales. There is a large body of literature on removing synchronization points from existing algorithms in the context of BSP computing and beyond. For example, many algorithms allow for the local detection of the global end of a superstep simply by comparing local information to the number of messages already received. This drives the cost of a global synchronisation, compared to the minimally required latency of communication, to zero. Yet also this minimal latency is expected to increase further for future supercomputer architectures and network interconnects; the BSP model, along with other models for parallel computation, require adaptation to cope with this trend. Multi-BSP is one BSP-based solution.
Algorithmic cost.
The cost of a superstep is determined as the sum of three terms:
Thus, the cost of one superstep for formula_16 processors:
formula_17
where formula_18 is the cost for the local computation in process formula_19, and formula_20 is the number of messages sent or received by process formula_19. Note that homogeneous processors are assumed here. It is more common for the expression to be written as formula_22 where formula_23 and formula_2 are maxima. The cost of the algorithm then, is the sum of the costs of each superstep.
formula_25
where formula_26 is the number of supersteps.
formula_27, formula_28, and formula_26 are usually modelled as functions, that vary with problem size. These three characteristics of a BSP algorithm are usually described in terms of asymptotic notation, e.g. formula_30.
Extensions and uses.
Interest in BSP has soared, with Google adopting it as a major technology for graph analytics at massive scale via Pregel and MapReduce. Also, with the next generation of Hadoop decoupling the MapReduce model from the rest of the Hadoop infrastructure, there are now active open-source projects to add explicit BSP programming, as well as other high-performance parallel programming models, on top of Hadoop. Examples are Apache Hama and Apache Giraph.
BSP has been extended by many authors to address concerns about BSP's unsuitability for modelling specific architectures or computational paradigms. One example of this is the decomposable BSP model. The model has also been used in the creation of a number of new programming languages and interfaces, such as Bulk Synchronous Parallel ML (BSML), BSPLib, Apache Hama, and Pregel.
Notable implementations of the BSPLib standard are the Paderborn University BSP library and the Oxford BSP Toolset by Jonathan Hill. Modern implementations include BSPonMPI (which simulates BSP on top of the Message Passing Interface), and MulticoreBSP (a novel implementation targeting modern shared-memory architectures). MulticoreBSP for C is especially notable for its capability of starting nested BSP runs, thus allowing for explicit Multi-BSP programming.