6.12 Speeding up the search for the absolute center In our
discussion of the absolutewenter problem, it was pointed out that the quantity
provides a lower bound for the value of m(x) on a link (p, q) [cf. (6.26)]. This bound provides a very convenient test that facilitates the search for the absolute center of a graph.
Another bound for m(x) has been developed recently, as follows. For the link (p, q), let r be the farthest node from p (r N) and s the farthest node from q(s N) [i.e., m(p) = d(p, r) and m(q) = d(q, s)]. The quantities that will be used to develop the new bound are d(p, s) and d(q, r). Clearly, the quantity Max [d(x, r), d(x, s)] provides a lower bound on m(x).