Abstract: Enumerating a number of good solutions to a problem has an increasing demand in recented research in computational science. In this paper, we presented a fixed-parameter enumeration algorithm for the 3-D Matching problem.More precisely, we developed an algorithm that, on a given set S of n weighted triples and two integers k and z, produces z "best" k-matchings in time O(5. 483kkn2z). Our algorithm is based on the recent improved color-coding techniques and the fixed-parameter enumeration framework. This result shows that the 3-D Matching problem is fixed parameter linearly cnumcrablc.

Key words: 3-D Matching, Fixed-parameter enumerable, Color-coding