Advanced Graph Algorithms
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This chapter discusses a selection of advanced graph algorithms. Section 12.1 presents an algorithm for finding the strongly connected components of a graph. After this, we will learn how to efficiently solve the 2SAT problem using the algorithm. Section 12.2 focuses on Eulerian and Hamiltonian paths. An Eulerian path goes through each edge of the graph exactly once, and a Hamiltonian path visits each node exactly once. While the concepts look quite similar at first glance, the computational problems related to them are very different. Section 12.3 first shows how we can determine the maximum flow from a source to a sink in a graph. After this, we will see how to reduce several other graph problems to the maximum flow problem. Section 12.4 discusses properties of depth-first search and problems related to biconnected graphs.