LogP machine

The LogP machine is a model for parallel computation.¹ It aims at being more practical than the PRAM model while still allowing for easy analysis of computation. The name is not related to the mathematical logarithmic function: Instead, the machine is described by the four parameters ${\displaystyle L}$, ${\displaystyle o}$, ${\displaystyle g}$ and ${\displaystyle P}$.

The LogP machine consists of arbitrarily many processing units with distributed memory. The processing units are connected through an abstract communication medium which allows point-to-point communication. This model is pair-wise synchronous and overall asynchronous.

The machine is described by the four parameters:

• ${\displaystyle L}$, the latency of the communication medium.
• ${\displaystyle o}$, the overhead of sending and receiving a message.
• ${\displaystyle g}$, the gap required between two send/receive operations. A more common interpretation of this quantity is as the inverse of the bandwidth of a processor-processor communication channel.
• ${\displaystyle P}$, the number of processing units.

Each local operation on each machine takes the same time ('unit time'). This time is called a processor cycle. The units of the parameters ${\displaystyle L}$, ${\displaystyle o}$ and ${\displaystyle g}$ are measured in multiples of processor cycles.