  We consider the enumeration problem of first-order queries over structures of
bounded degree. It was shown that this problem is in the Constant-Delaylin
class. An enumeration problem belongs to Constant-Delaylin if for an input of
size n it can be solved by: - an O(n) precomputation phase building an index
structure, - followed by a phase enumerating the answers with no repetition and
a constant delay between two consecutive outputs. In this article we give a
different proof of this result based on Gaifman's locality theorem for
first-order logic. Moreover, the constants we obtain yield a total evaluation
time that is triply exponential in the size of the input formula, matching the
complexity of the best known evaluation algorithms.
