What is included with this book?
Foreword | |
Euclidean Steiner Problem | p. 1 |
Introduction | p. 3 |
Historical Background | p. 3 |
Some Basic Notions | p. 5 |
Some Basic Properties | p. 6 |
Full Steiner Trees | p. 8 |
Steiner Hulls and Decompositions | p. 9 |
The Number of Steiner Topologies | p. 13 |
Computational Complexity | p. 14 |
Physical Models | p. 16 |
Exact Algorithms | p. 21 |
The Melzak Algorithm | p. 22 |
A Linear-Time FST Algorithm | p. 23 |
Two Ideas on the Melzak Algorithm | p. 25 |
A Numerical Algorithm | p. 26 |
Pruning | p. 27 |
The GEOSTEINER Algorithm | p. 28 |
The Negative Edge Algorithm | p. 30 |
The Luminary Algorithm | p. 32 |
The Steiner Ratio | p. 37 |
Lower Bounds of [rho] | p. 38 |
The Small n Case | p. 39 |
The Variational Approach | p. 41 |
The Steiner Ratio Conjecture as a Maximin Problem | p. 42 |
Critical Structures | p. 44 |
A Proof of the Steiner Ratio Conjecture | p. 45 |
Heuristics | p. 51 |
Minimal Spanning Trees | p. 52 |
Improving the FIST | p. 52 |
Greedy Trees | p. 54 |
An Annealing Algorithm | p. 55 |
A Partitioning Algorithm | p. 57 |
Few's Algorithms | p. 57 |
A Graph Approximation Algorithm | p. 58 |
k-Size Quasi-Steiner Trees | p. 59 |
Other Heuristics | p. 60 |
Special Terminal-Sets | p. 63 |
Four Terminals | p. 63 |
Cocircular Terminals | p. 66 |
Co-path Terminals | p. 68 |
Terminals on Lattice Points | p. 71 |
Two Related Results | p. 73 |
Generalizations | p. 77 |
d-Dimensional Euclidean Spaces | p. 77 |
Cost of Edge | p. 80 |
Terminal Clusters and New Terminals | p. 83 |
k-SMT | p. 84 |
Obstacles | p. 85 |
Steiner Problem in Networks | p. 91 |
Introduction | p. 93 |
Applications | p. 94 |
Definitions | p. 95 |
Trivial Special Cases | p. 97 |
Problem Reformulations | p. 97 |
Complexity | p. 100 |
Reductions | p. 103 |
Exclusion Tests | p. 104 |
Inclusion Tests | p. 112 |
Integration of Tests | p. 118 |
Effectiveness of Reductions | p. 122 |
Exact Algorithms | p. 125 |
Spanning Tree Enumeration Algorithm | p. 125 |
Degree-Constrained Tree Enumeration Algorithm | p. 126 |
Topology Enumeration Algorithm | p. 127 |
Dynamic Programming Algorithm | p. 128 |
Branch-and-Bound Algorithm | p. 130 |
Mathematical Programming Formulations | p. 132 |
Linear Relaxations | p. 137 |
Lagrangean Relaxations | p. 138 |
Benders' Decomposition Algorithm | p. 141 |
Set Covering Algorithm | p. 143 |
Summary and Computational Experience | p. 144 |
Heuristics | p. 151 |
Path Heuristics | p. 151 |
Tree Heuristics | p. 156 |
Vertex Heuristics | p. 164 |
Contraction Heuristic | p. 169 |
Dual Ascent Heuristic | p. 171 |
Set Covering Heuristic | p. 171 |
Summary and Computational Experience | p. 172 |
Polynomially Solvable Cases | p. 177 |
Series-Parallel Networks | p. 177 |
Halin Networks | p. 180 |
k-Planar Networks | p. 181 |
Strongly Chordal Graphs | p. 185 |
Generalizations | p. 189 |
Steiner Trees in Directed Networks | p. 189 |
Weighted Steiner Tree Problem | p. 190 |
Steiner Forest Problem | p. 191 |
Hierarchical Steiner Tree Problem | p. 191 |
Degree-Dependent Steiner Tree Problem | p. 192 |
Group Steiner Tree Problem | p. 193 |
Multiple Steiner Trees Problem | p. 195 |
Multiconnected Steiner Network Problem | p. 196 |
Steiner Problem in Probabilistic Networks | p. 198 |
Realization of Distance Matrices | p. 199 |
Other Steiner-Like Problems | p. 199 |
Rectilinear Steiner Problem | p. 203 |
Introduction | p. 205 |
Definitions | p. 205 |
Basic Properties | p. 208 |
A Characterization of RSMTs | p. 211 |
Problem Reductions | p. 212 |
Extremal Results | p. 215 |
Computational Complexity | p. 218 |
Exact Algorithm | p. 218 |
Heuristic Algorithms | p. 221 |
Heuristics Using a Given RMST | p. 221 |
Heuristics Based on MST Algorithms | p. 229 |
Computational Geometry Paradigms | p. 233 |
Other Heuristics | p. 237 |
Polynomially Solvable Cases | p. 243 |
Terminals on a Rectangular Boundary | p. 243 |
Rectilinearly Convex Boundary | p. 251 |
Layered Terminal Sets | p. 253 |
Generalizations | p. 257 |
Rectangle Trees | p. 257 |
Rectilinear Steiner Arborescences | p. 258 |
Steiner Trees in Hypercubes | p. 261 |
Higher Dimensions | p. 263 |
Routing | p. 267 |
Introduction | p. 267 |
Heuristics for Single Nets | p. 270 |
Heuristics for Multiple Nets | p. 276 |
Multiple Layers | p. 280 |
Other Steiner Problems | p. 285 |
Steiner Trees in Other Metric Spaces | p. 287 |
Minkowski Spaces | p. 287 |
Minkowski Planes and l[subscript p] Metrics | p. 289 |
[lambda]-Geometry and Hexagonal Plane | p. 291 |
Better Heuristics for Arbitrary Metric Spaces | p. 295 |
Bounds for the Performance Ratios of Quasi-STs | p. 297 |
Phylogenetic Trees | p. 301 |
Definitions | p. 302 |
Compatibility Methods | p. 304 |
Maximum Parsimony Methods | p. 306 |
Wagner Parsimony Method | p. 308 |
Other Maximum Parsimony Methods | p. 313 |
Maximum Likelihood Methods | p. 314 |
Distance Methods | p. 315 |
Subject Index | p. 323 |
Author Index | p. 335 |
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