Cunningham's Rule constructions because they tend to average out how many times a variable pivots. It has recently been shown by David Avis and Oliver Friedmann that there is a family of linear programs on which the simplex algorithm equipped with Cunningham's rule requires exponential time. Cunningham's Rule In mathematical optimization, Cunningham's rule (also known as least recently considered rule or round-robin rule) is an algorithmic refinement of the simplex method for linear optimization. The rule was proposed 1979 by W.H. Cunningham to defeat the deformed hypercube constructions by Klee and Minty et. al. (see, e.g. Klee–Minty cube). Cunningham's rule assigns a
Phonological rule most general way possible. Thus, the intervocalic alveolar flapping described above can be formalized as The rule given above for intervocalic alveolar flapping describes what sound is changed, what the sound changes to, and where the change happens (in other words, what the "environment" is that triggers the change). The illustration below presents the same rule, with each of its parts labelled and described. Taken together and read from left to right, this notation of the rule for intervocalic alveolar flapping states that any alveolar stop consonant (/t/ or /d/) becomes a tap ([ɾ]) in the environment where it is