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Shortest Paths,ll present some useful theoretical concepts (e.g.,?the Bellman equations, shortest path threes, and path algebras) as well as the most important algorithms for finding shortest paths (in?particular, breadth first search, the algorithm of Dijkstra, and the algorithm of Floyd and Warshall). We also di

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The Network Simplex Algorithm,al interest admit easy transformations to this problem. Throughout this book, we emphasize the graph theoretical aspects of combinatorial optimization while avoiding the theory of linear programming as much as possible. In view of this philosophy, it is very fortunate that the network simplex algori

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Weighted Matchings,he corresponding polytope, and ultimately to the total unimodularity of the incidence matrix of a bipartite graph. In this context, the reason why the determination of maximal matchings (weighted or not) is considerably more difficult for arbitrary graphs than for bipartite ones will become apparent

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A Hard Problem: The TSP,on, local search, and complete enumeration. We shall explain these methods only for the TSP, but they are typical for dealing with hard problems in general. We will also brie y explain the idea of a further extremely important approach—via polyhedra—to solving hard problems and present a list of not

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Forschung Erziehungswissenschaftl alternative approach of taking Philip Hall’s marriage theorem—which we will treat in Sect.?.—as the starting point of transversal theory, this way of proceeding has a distinct advantage: it also yields algorithms allowing explicit constructions for the objects in question.

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