The oldest result contained in the compendium is a 4/3-approximation
algorithm for MINIMUM EDGE COLORING due to [14]. Actually, this
algorithm is optimal since in [8] it is shown that, for
any
,
no
-approximation algorithm exists
for this problem. It is worth pointing out that in neither of the
above two references the notion of approximation algorithm is
explicitly used.
The second oldest result, instead, is due to [9] which is
widely considered the starting point of the theory of approximation
algorithm (indeed, the compendium contains four results due to
this paper). In particular, the above reference contains a -approximation algorithm for MINIMUM SET COVER: 25 years later it has
been proved that this algorithm is optimal [13]!