Parallelization of computations for generating combinations

Abstract

An effective sequential algorithm and two parallel algorithms for generating combinations without repetitions of m out n of objects, represented by Boolean vectors, are proposed. One of them allows one to calculate starting and ending combinations for the subset, generated by each computing processor. The second algorithm firstly generates short (m-component) vectors on several computing processors. After that, by using special [n/m]-component vectors, it connects the short vectors into ncomponent Boolean vectors, each of which containing of exactly m units.