Random Combinatorial Objects

Abstract

Some applications demand that random combinatorial objects be generated: by definition, a combinatorial object is an object that can be put into one-to-one correspondence with a finite set of integers. The main difference with discrete random varlate generation is that the one-to-one mapping is usually complicated, so that it may not be very efficient to generate a random integer and then determine the object by using the one-to-one mapping. Another characteristic is the size of the problem: typically, the number of different objects is phenomenally large. A final distinguishing feature is that most users are interested in the uniform distribution over the set of objects.