By R.M.R. Lewis
ISBN-10: 3319257285
ISBN-13: 9783319257280
ISBN-10: 3319257307
ISBN-13: 9783319257303
This booklet treats graph colouring as an algorithmic challenge, with a powerful emphasis on useful purposes. the writer describes and analyses many of the best-known algorithms for colouring arbitrary graphs, targeting no matter if those heuristics provides optimum strategies sometimes; how they practice on graphs the place the chromatic quantity is unknown; and whether or not they can produce higher recommendations than different algorithms for particular types of graphs, and why.
The introductory chapters clarify graph colouring, and limits and positive algorithms. the writer then indicates how complex, sleek concepts should be utilized to vintage real-world operational examine difficulties similar to seating plans, activities scheduling, and collage timetabling. He contains many examples, feedback for additional analyzing, and historic notes, and the publication is supplemented by means of an internet site with a web suite of downloadable code.
The e-book can be of price to researchers, graduate scholars, and practitioners within the parts of operations learn, theoretical desktop technological know-how, optimization, and computational intelligence. The reader must have common wisdom of units, matrices, and enumerative combinatorics.
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Additional resources for A guide to graph colouring : algorithms and applications
Sample text
6 About This Book As we have seen in this introductory chapter, this book focusses on the problem of colouring the vertices of a graph. Sometimes the term “graph colouring” is also applied to the task of colouring the edges of a graph or the faces of a graph. However, as we shall see in Chapter 5, edge and face colouring problems can easily be transformed into an equivalent vertex colouring problem via the concepts of line graphs and dual graphs respectively. Consequently, unless explicitly stated other- 22 1 Introduction to Graph Colouring wise, the term “graph colouring” in this book refers exclusively to the problem of vertex colouring.
If there is more than one vertex with maximal saturation degree, then ties are broken by choosing the vertex among these with the largest degree. Any further ties can then be broken randomly. The idea behind the maximum saturation degree heuristic is that it prioritises vertices that are seen to be the most “constrained”—that is, vertices that currently have the fewest colour options available to them. Consequently, these “more constrained” vertices are dealt with by the algorithm first, allowing the less constrained vertices to be coloured later.
A more rigorous approach to measuring computational effort involves examining the number of atomic operations performed by an algorithm during execution. 6 About This Book 23 of a vector, these are usually considered to be the constant-time operations of comparing two elements and swapping two elements. For others, such as the bin packing problem, where we seek to partition a set of weighted items into a set of bins with limited capacity, these are often considered to be the operations of looking up some feature of the problem instance, such as referencing the weight of one of the items.
A guide to graph colouring : algorithms and applications by R.M.R. Lewis
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