Graph Separators, with Applications

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Springer Science & Business Media, Jun 30, 2001 - Computers - 257 pages
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Graph Separators with Applications is devoted to techniques for obtaining upper and lower bounds on the sizes of graph separators - upper bounds being obtained via decomposition algorithms. The book surveys the main approaches to obtaining good graph separations, while the main focus of the book is on techniques for deriving lower bounds on the sizes of graph separators. This asymmetry in focus reflects our perception that the work on upper bounds, or algorithms, for graph separation is much better represented in the standard theory literature than is the work on lower bounds, which we perceive as being much more scattered throughout the literature on application areas. Given the multitude of notions of graph separator that have been developed and studied over the past (roughly) three decades, there is a need for a central, theory-oriented repository for the mass of results. The need is absolutely critical in the area of lower-bound techniques for graph separators, since these techniques have virtually never appeared in articles having the word `separator' or any of its near-synonyms in the title. Graph Separators with Applications fills this need.
  

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Contents

A Technical Introduction
1
12 Basic Notions and Notation
2
13 Interesting Graph Families
4
14 Graph Separators
12
15 Graph Embeddings
27
16 QuasiIsometric Graph Families
33
17 Sources
44
Applications of Graph Separators
47
35 Network Flow Approaches to Graph Separation
130
36 Heuristic Approaches to Graph Separation
147
37 Sources
156
LowerBound Techniques
159
42 Packing Arguments for Bounding SeparationWidth
162
43 Congestion Arguments for Bounding SeparationWidth
188
44 A Technique for Complete Trees
209
45 InformationTransfer Arguments
218

22 Nonserial Dynamic Programming
49
23 Graph Embeddings via Separators
53
24 Laying Out VLSI Circuits
68
25 Strongly Universal Interval Hypergraphs
82
Register Allocation and Processor Scheduling
92
27 Sources
94
UpperBound Techniques
99
32 NPCompleteness
101
33 Topological Approaches to Graph Separation
109
34 Geometric Approaches to Graph Separation
121
46 Sources
223
Applications of Graph Separators Revisited
227
A3 Laying Out VLSI Circuits
232
A4 Strongly Universal Interval Hypergraphs
235
A5 Pebbling Games
239
A6 Sources
240
Bibliography
241
About the Authors
251
INDEX
253
Copyright

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