Global Methods for Combinatorial Isoperimetric Problems

This text explores global methods in combinatorial optimization and is suitable for graduate students and researchers.

L. H. Harper (Author)

9780521832687, Cambridge University Press

Hardback, published 9 February 2004

250 pages
22.9 x 15.2 x 1.7 cm, 0.54 kg

"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

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.

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.

Subject Areas: Mathematical theory of computation [UYA], Combinatorics & graph theory [PBV]