Global Methods for Combinatorial Isoperimetric Problems

L. H. Harper (University of California, Riverside)

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English

Cambridge University Press
16 December 2010

Combinatorics & graph theory; Mathematical theory of computation

Series: Cambridge Studies in Advanced Mathematics

Certain constrained combinatorial optimization problems have a natural analogue in the continuous setting of the classical isoperimetric problem. The study of so called combinatorial isoperimetric problems exploits similarities between these two, seemingly disparate, settings. This text focuses on global methods. This means that morphisms, typically arising from symmetry or direct product decomposition, are employed to transform new problems into more restricted and easily solvable settings whilst preserving essential structure. This book is based on Professor Harper's many years' experience in teaching this subject and is ideal for graduate students entering the field. The author has increased the utility of the text for teaching by including worked examples, exercises and material about applications to computer science. Applied systematically, the global point of view can lead to surprising insights and results, and established researchers will find this to be a valuable reference work on an innovative method for problem solving.

By: L. H. Harper (University of California Riverside)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 90
Dimensions: Height: 229mm, Width: 152mm, Spine: 14mm
Weight: 370g
ISBN: 9780521183833
ISBN 10: 0521183839
Series: Cambridge Studies in Advanced Mathematics
Pages: 250
Publication Date: 16 December 2010
Audience: College/higher education , Further / Higher Education
Format: Paperback
Publisher's Status: Active

1. The edge-isoperimetric problem; 2. The minimum path problem; 3. Stabilization and compression; 4. The vertex-isoperimetric problem; 5. Stronger stabilization; 6. Higher compression; 7. Isoperimetric problems on infinite graphs; 8. Isoperimetric problems on complexes; 9. Morphisms for MWI problems; 10. Passage to the limit; 11. Afterword; 12. The classical isoperimetric problem.

Reviews for Global Methods for Combinatorial Isoperimetric Problems

It is a very nice and useful book, written by a real expert in the field. I believe that both specialists in the area and mathematicians with other backgrounds will find lots of new interesting material in this book. Igor Shparlinski, Mathematics of Computation