Graph Separators, With Applications

by Rosenberg, Arnold L.; Heath, Lenwood S.

• ISBN13: 9780306464645
• ISBN10: 0306464640
• Format: Hardcover
• Copyright: 2000-12-01
• Publisher: Plenum Pub Corp

Summary

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.

Table of Contents

A Technical Introduction	1	(46)
Introduction	1	(1)
Basic Notions and Notation	2	(2)
Interesting Graph Families	4	(8)
Graph Separators	12	(15)
Graph Embeddings	27	(6)
Quasi--Isometric Graph Families	33	(11)
Sources	44	(3)
Applications of Graph Separators	47	(52)
Introduction	47	(2)
Nonserial Dynamic Programming	49	(4)
Graph Embeddings via Separators	53	(15)
Laying Out VLSI Circuits	68	(14)
Strongly Universal Interval Hypergraphs	82	(10)
Pebbling Games: Register Allocation and Processor Scheduling	92	(2)
Sources	94	(5)
Upper-Bound Techniques	99	(60)
Introduction	101	(1)
NP-Completeness	101	(8)
Topological Approaches to Graph Separation	109	(12)
Geometric Approaches to Graph Separation	121	(9)
Network Flow Approaches to Graph Separation	130	(17)
Heuristic Approaches to Graph Separation	147	(9)
Sources	156	(3)
Lower-Bound Techniques	159	(68)
Overview of Lower-Bound Techniques	159	(3)
Packing Arguments for Bounding Separation-Width	162	(26)
Congestion Arguments for Bounding Separation-Width	188	(21)
A Technique for Complete Trees	209	(9)
Information-Transfer Arguments	218	(5)
Sources	223	(4)
Appendix A. Applications of Graph Separators, Revisited	227	(16)
A.1. Introduction	227	(1)
A.2. Graph Embeddings via Separators	227	(5)
A.3. Laying Out VLSI Circuits	232	(3)
A.4. Strongly Universal Interval Hypergraphs	235	(4)
A.5. Pebbling Games	239	(1)
A.6. Sources	240	(3)
Bibliography	243	(10)
About the Authors	253	(2)
Index	255