Abstract
The weighted m - d matching and m - set packing problems ( m ≥ 3 ) are usually solved through approximation algorithms. In this paper, we define the parameterized versions of these problems and study their algorithms. For the weighted m - set packing problem, we develop a parameterized algorithm of running time O ( 12 . 8 m k n O ( 1 ) ) , which is based on the recently improved color-coding technology and dynamic programming. By refining the techniques, we also develop a more efficient parameterized algorithm of running time O ( 12 . 8 ( m − 1 ) k n O ( 1 ) ) for the weighted m - d matching problem, which is a restricted version of the weighted m - set packing problem.
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