The.Algorithm.Design.Manual.Springer-Verlag.1998

Graph Algorithms
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Graph Algorithms
A graph G=(V,E) consists of a set of vertices V together with a set E of vertex pairs or edges. Graphs are
important because they can be used to represent essentially any relationship. For example, graphs can
model a network of roads, with cities as vertices and roads between cities as edges, as shown in Figure
. Electronic circuits can also be modeled as graphs, with junctions as vertices and components as
edges.
Figure: Modeling road networks and electronic circuits as graphs
The key to understanding many algorithmic problems is to think of them in terms of graphs. Graph
theory provides a language for talking about the properties of graphs, and it is amazing how often messy
applied problems have a simple description and solution in terms of classical graph properties.
Designing truly novel graph algorithms is a very difficult task. The key to using graph algorithms
effectively in applications lies in correctly modeling your problem as a standard graph property, so you
can take advantage of existing algorithms. Becoming familiar with many different graph algorithmic
problems is more important than understanding the details of particular graph algorithms, particularly
since Part II of this book can point you to an implementation as soon as you know the name of your
problem.
In this chapter, we will present basic data structures and traversal operations for graphs, which will
enable you to cobble together solutions to rudimentary graph problems. We will also describe more
sophisticated algorithms for problems like shortest paths and minimum spanning trees in some detail. But
we stress the primary importance of correctly modeling your problem. Time spent browsing through the
catalog now will leave you better informed of your options when a real job arises.
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