peroperation

Peroperation is a theoretical cost model used in computer science to quantify the resource usage of an algorithm by assigning a fixed cost to each elementary operation. In a peroperation model, the total cost is the number of elementary operations performed, multiplied by a constant unit cost, typically normalized to one. This approach highlights the count of operations rather than data size or memory traffic and is commonly used to obtain simple, architecture-agnostic estimates of running time in asymptotic analysis.

Definition and scope: An elementary operation refers to a basic step such as an arithmetic calculation, a comparison, or an assignment, with the exact set defined by the analyst. The model assumes uniform cost for all such operations, and more complex actions may be decomposed into sequences of elementary steps to fit the model. It abstracts away hardware details like cache behavior, pipelining, and parallel execution, focusing on the algorithmic structure.

Applications: Peroperation analysis is used in teaching to illustrate how algorithms scale with operation counts, in theoretical work to derive bounds, and in some microbenchmarking or performance modeling to compare implementations when operation cost is roughly uniform.

Limitations: The unit-cost assumption is often unrealistic on modern hardware, where costs vary with memory access, data movement, and parallelism. Real performance depends on data access patterns, caching, branch prediction, and architecture-dependent optimizations, which a pure peroperation model cannot capture. Hence results should be treated as rough, high-level estimates.

Relation to other models: It is related to the unit-cost RAM model, differing mainly in how the operation set is defined. It is one of several operation-counting approaches used in algorithm analysis.

See also: computational complexity, RAM model, unit-cost model, operation counting.