An edge dominating set of a graph G = (V, E) is a subset M of edges
such that each edge in E-M is incident to at least one edge in M. In
this paper, we consider the parameterized edge dominating set problem
which asks us to test whether a given graph has an edge dominating set
with size bounded from above by an integer k or not, and we design an O
^*(2.2351^k)-time and polynomial-space algorithm. This is an improvement
over the previous best time bound of O^*(2.3147^k). We also show that a
related problem: the parameterized weighted edge dominating set problem
can be solved in O^*(2.2351^k) time and polynomial space.