  We study the relation type question, raised by C. Huneke, which asks whether
for a complete equidimensional local ring R there exists a uniform bound for
the relation type of parameter ideals. Wang gave a positive answer to this
question when the non-Cohen-Macaulay locus of R, denoted by NCM(R), has
dimension zero. We first present an example, due to the first author, which
gives a negative answer to the question when dim NCM(R) is at least 2. The
major part of our work then is to investigate the remaining case, i.e., when
dim NCM(R) = 1. We introduce the notion of homology multipliers and show that
the question has a positive answer when R/A(R) is a domain, where A(R) is the
ideal generated by all homology multipliers in R. In a more general context, we
also discuss many interesting properties of homology multipliers.
