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Global Methods for Combinatorial Isoperimetric Problems [Minkštas viršelis]

(University of California, Riverside)
  • Formatas: Paperback / softback, 250 pages, aukštis x plotis x storis: 229x152x14 mm, weight: 370 g, Worked examples or Exercises
  • Serija: Cambridge Studies in Advanced Mathematics
  • Išleidimo metai: 16-Dec-2010
  • Leidėjas: Cambridge University Press
  • ISBN-10: 0521183839
  • ISBN-13: 9780521183833
Kitos knygos pagal šią temą:
  • Formatas: Paperback / softback, 250 pages, aukštis x plotis x storis: 229x152x14 mm, weight: 370 g, Worked examples or Exercises
  • Serija: Cambridge Studies in Advanced Mathematics
  • Išleidimo metai: 16-Dec-2010
  • Leidėjas: Cambridge University Press
  • ISBN-10: 0521183839
  • ISBN-13: 9780521183833
Kitos knygos pagal šią temą:
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.

Recenzijos

"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

Daugiau informacijos

This text explores global methods in combinatorial optimization and is suitable for graduate students and researchers.
Preface ix
1 The edge-isoperimetric problem
1(19)
1.1 Basic definitions
1(1)
1.2 Examples
1(8)
1.3 Application to layout problems
9(9)
1.4 Comments
18(2)
2 The minimum path problem
20(12)
2.1 Introduction
20(1)
2.2 Algorithms
21(3)
2.3 Reduction of wirelength to minpath
24(1)
2.4 Pathmorphisms
25(4)
2.5 Comments
29(3)
3 Stabilization and compression
32(20)
3.1 Introduction
32(1)
3.2 Stabilization
32(12)
3.3 Compression
44(5)
3.4 Comments
49(3)
4 The vertex-isoperimetric problem
52(16)
4.1 Definitions and examples
52(1)
4.2 Stabilization and VIP
53(3)
4.3 Compression for VIP
56(3)
4.4 Optimality of Hales numbering
59(2)
4.5 Applications to layout problems
61(5)
4.6 Comments
66(2)
5 Stronger stabilization
68(35)
5.1 Graphs of regular solids
68(6)
5.2 A summary of Coxeter theory
74(5)
5.3 The structure of stability orders
79(3)
5.4 Calculating stability orders
82(3)
5.5 Into the fourth dimension
85(11)
5.6 Extended stabilization
96(4)
5.7 Comments
100(3)
6 Higher compression
103(25)
6.1 Additivity
103(4)
6.2 The MWI problem
107(2)
6.3 The Ahlswede-Cai theorem
109(6)
6.4 The Bezrukov-Das-Elsasser theorem
115(10)
6.5 Comments
125(3)
7 Isoperimetric problems on infinite graphs
128(17)
7.1 Euclidean tessellations
129(13)
7.2 Comments
142(3)
8 Isoperimetric problems on complexes
145(24)
8.1 Minimum shadow problems
146(6)
8.2 Steiner operations for MSP
152(10)
8.3 Scheduling problems
162(4)
8.4 Comments
166(3)
9 Morphisms for MWI problems
169(27)
9.1 MWI-morphisms
169(4)
9.2 Examples
173(7)
9.3 Application I: The pairwise product of Petersen graphs
180(2)
9.4 Application II: The EIP on the 600-vertex
182(3)
9.5 The calculation for V600
185(9)
9.6 Comments
194(2)
10 Passage to the limit
196(21)
10.1 The Bollobas-Leader theorem
196(6)
10.2 The Kleitman-West problem
202(6)
10.3 VIP on the Hamming graph
208(1)
10.4 Sapozhenko's problem
209(4)
10.5 Comments
213(4)
Afterword 217(2)
Appendix: The classical isoperimetric problem 219(4)
References 223(6)
Index 229