fixedk

Fixedk is a term used across mathematics and computer science as a concise label for a parameter k that is kept constant during analysis or computation. There is no universally accepted definition for fixedk; its precise meaning depends on context. In theoretical computer science, fixedk commonly appears in the study of fixed-parameter tractability. When a problem is parameterized by k and an algorithm runs in time f(k)·poly(n), with n the input size, the value of k is treated as fixed to obtain tractable performance for small k. In this setting fixedk denotes that k is not part of the asymptotic input size.

In mathematics, fixedk can designate a constant integer employed in a lemma or construction. For example, a statement might hold for all integers n with n ≥ N(k), where k is fixed. In practical software and data processing, fixedk is frequently used as a variable name for a tunable parameter such as a neighborhood size, a number of clusters, or a grid resolution, with k chosen once per run and not altered during computation.

Usage note: fixedk is not a formal, universally standardized term. Authors may write it as fixed-k or simply k fixed, depending on style. When encountering the term, readers should rely on the surrounding definitions to determine what parameter k represents and whether it is held constant or varied across instances.