By Robert Sedgewick
Graph algorithms are serious for more than a few functions, resembling community connectivity, circuit layout, scheduling, transaction processing, and source allocation. This paintings offers many algorithms and their causes. it is usually targeted figures, with accompanying remark.
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Additional info for Algorithms in C, Part 5: Graph Algorithms
A directed cycle in a digraph is a cycle in which all adjacent vertex pairs appear in the order indicated by (directed) graph edges. A directed acyclic graph (DAG), is a digraph that has no directed cycles. A DAG (an acyclic digraph) is not the same as a tree (an acyclic undirected graph). Occasionally, we refer to the underlying undirected graph of a digraph, meaning the undirected graph defined by the same set of edges, but where these edges 15 are not interpreted as directed. Chapters 20 through 22 are generally concerned with algorithms for solving various computational problems associated with graphs in which other information is associated with the vertices and edges.
One of the connected components is a tree (right). The graph has many cycles, one of which is highlighted in the large connected component (left). The diagram also depicts a spanning tree in the small connected component (center). The graph as a whole does not have a spanning tree, because it is not connected. We adopt the convention that each single vertex is a path of length 0 (a path from the vertex to itself with no edges on it, which is different from a self-loop). Apart from this convention, in a graph with no parallel edges and no self-loops, a pair of vertices uniquely determines an edge, paths must have on them at least two distinct vertices, and cycles must have on them at least three distinct edges and three distinct vertices.
That representation, however, does not provide the flexibility that we need to perform efficiently the basic graph-processing operations that we shall be studying. In this book, we generally work with static graphs, which have a fixed number of vertices V and edges E. Generally, we build the graphs by executing E calls to GRAPHinsertE, then process them by calling some ADT function that takes a graph as argument and returns some information about that graph. Dynamic problems, where we intermix graph processing with edge and vertex insertion and removal, take us into the realm of online algorithms (also known as dynamic algorithms), which present a different set of challenges.
Algorithms in C, Part 5: Graph Algorithms by Robert Sedgewick