L. H. HarperCambridge University PressEdition: Reissue, 12/16/2010EAN 9780521183833, ISBN10: 0521183839Paperback, 250 pages, 22.9 x 15.2 x 1.4 cmLanguage: EnglishCertain 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 problem2. The minimum path problem3. Stabilization and compression4. The vertex-isoperimetric problem5. Stronger stabilization6. Higher compression7. Isoperimetric problems on infinite graphs8. Isoperimetric problems on complexes9. Morphisms for MWI problems10. Passage to the limit11. Afterword12. The classical isoperimetric problem.
