CHAPTER 10 - Graph Algorithms

Abstract

This chapter provides an overview of the common paradigms and results in graph algorithms with an emphasis on the more recent developments in the field. Three main areas of concern in graph algorithms are: the representation and exploration of graphs, basic structure algorithms for graphs, and algorithms for some common optimalization problems on graphs. When a computational problem is modeled in terms of graphs, the resulting graphs should be generated and represented in some form to facilitate the operations of an algorithm. The desired representation can be an abstract data structure that supports certain operations efficiently, or it can be a concrete display of the graph that allows visual inspection and interactive manipulations. Graph theory provides a wealth of results about the structure of graphs. In graph algorithms, the aim is to identify substructures or properties algorithmically, by a program that can be run on every admissible input graph. The richest source of computational problems on graphs is the theory of combinatorial optimization, where the underlying structures usually are networks. A network is a graph in which the edges are labeled by edge weights or capacities.