The first description of a generalized backtrack search algorithm was in
[35]. Let us first define a restricted version of the search
problem.
Search problem:
Given a collection of sets of candidates 
and
a boolean compatibility function 
defined for all 
and 
, find an m-tuple 
with 
such that 
is true for all 
.
The m-tuple satisfying the above condition is called a solution.
The term compatibility was first introduced by Carter in 1974
[9]. This version is restricted because the compatibility
function is only defined on ordered pairs rather than on all k-tuples,
.
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