Combiners in Hadoop MapReduce

A combiner function in MapReduce has the same form as the reduce function (and is an implementation of the Reducer interface), except its output types are the intermediate key and value types (K₂ and V₂), so they can feed the reduce function:

combiner: (K₂, list(V₂)) → list(K₂, V₂)

Often the combiner and reduce functions are the same, in which case K₃ is the same as K₂, and V₃ is the same as V₂. On the other hand, Hadoop reserves the right to use combiners at its discretion. This means that a combiner may be invoked zero, one, or multiple times. Hence, the correctness of a MapReduce algorithm shouldn't depend on computations performed by the combiner or depend on them even being run at all.

Guidance for Scientific Writing

The Structure, Format, Content, and Style of a Journal-Style Scientific Paper

Typesetting mathematics for science and technology according to ISO 31/XI

According to the standard, constants like i and Euler's e, and the differential operator d should be upright. However, these typesetting rules seem to be ignored by many respected authors and publishers. See this thread for some interesting discussions on this issue: What's the proper way to typeset a differential operator? For those looking for an easy solution, one of the re-posts there suggests to typeset a math paper in Latex using package commath.