The concept of reduction operators—in which many or all elements of an array are reduced into one single result—is closely associated with concurrent and parallel programming. Specifically, because of the associative and communicative nature of the operators, concurrency and parallelism can be applied to greatly improve their execution time.

This chapter discusses the theoretical concurrent approach to designing and writing a reduction operator from the perspective of programmers and developers. From here, this chapter also makes connections to similar problems that can be solved using concurrency in similar ways.

The following topics will be covered in this chapter:

• The concept of a reduction operator in computer science
• The communicative and associative properties of reduction operators, and therefore the reason why concurrency can be applied
• How to identify problems that are equivalent to a reduction operator and how to apply concurrent programming in such cases