Structure analysis of some generalizations of matchings and matroids under algorithmic aspects Combinatorial optimization problems whose underlying structures are matchings or matroids are well known to be solvable with efficient algorithms. Matroids can even be characterized by a simple greedy algorithm. In the first part of this thesis some generalizations of matroids which allow the ground set to be partially ordered are considered. In particular it will be shown that a special type of lattice polyhedra for which Dietrich and Hoffman recently established a dual greedy algorithm can be reduced to ordinary polymatroids. Moreover strong exchange structures Gauss greedoids and Delta matroids will be extended from Boolean lattices to general distributive lattices and the resulting structures will be characterized by certain greedy type algorithms. While a matching of maximal size can be determined by a polynomial algorithm the dual problem of finding a vertex cover of minimal size in general graphs is one of the hardest problems in combinatorial optimization. However in case the graph belongs to the class of K\\ onig Egerv\\ary graphs a maximum matching can be used to construct a minimum vertex cover ...