The Steiner ratio
By: by Dietmar Cieslik.
Series: Combinatorial optimization -- v. 10
Publisher: Kluwer Academic Pub.
Published: 2001
Place of publication: Dordrecht; Boston
Language: eng
Number of pages: 244
Subjects: Steiner systems.
Notes: Includes bibliographical references (p. 223-239) and index.
Table of contents: title: Machine generated contents note: I; title: I; title: 1 THE HISTORICAL GENESIS; title: 1.1 The Past; title: 1.2 The Present; title: 1.3 The Future; title: 2 NETWORKS, SPACES AND ALGORITHMS; title: 2.1 Networks; title: 2.2 Spaces; title: 2.3 The Algorithmic Complexity of finding a Minimum Span-; title: ning Tree; title: 2.4 Steiner's Problem; title: 3 SHORTEST TREES IN METRIC SPACES - A; title: SURVEY; title: 3.1 Basic Properties of Steiner Minimal Trees in metric spaces; title: 3.2 The Vertex-Degrees of shortest trees in Banach-Minkowski; title: spaces; title: 3.3 The location of the Steiner points - Fermat's Problem; title: 3.4 Examples; title: 4 THE STEINER RATIO OF METRIC SPACES; title: 4.1 The range of the Steiner ratio; title: 4.2 Approximations; title: 4.3 The Steiner ratio of finite metric spaces; title: 4.4 The space of all words: Phylogenetic spaces; title: 5 THE STEINER RATIO OF BANACH-; title: MINKOWSKI SPACES; title: 5.1 Basic Properties; title: 5.2 The Decomposition of SMT's; title: 5.3 A Derivation of the Steiner ratio; title: 5.4 Direct Calculations for Lp-planes; title: 5.5 Direct Calculations for C3; title: 5.6 Direct Calculations for higher-dimensional Lp-spaces; title: 6 EUCLIDEAN SPACES; title: 6.1 Nontrivial lower and upper bounds; title: 6.2 The Euclidean plane; title: 6.3 The higher-dimensional case; title: 6.4 The three-dimensional case; title: 7 THE STEINER RATIO OF NEIGHBOURED; title: SPACES; title: 7.1 Neighboured Banach-Minkowski spaces; title: 7.2 Metrics in the Hyperspace; title: 7.3 Estimating Steiner ratios using the Banach-Mazur distance; title: 7.4 Estimating Steiner ratios using the Hausdorff distance; title: 8 BANACH-MINKOWSKI PLANES; title: 8.1 The Steiner ratio of the rectilinear plane; title: 8.2 The Steiner ratio of A-geometries; title: 8.3 A sharp lower bound for the Steiner ratio; title: 8.4 The range of the Steiner ratio in planes; title: 8.5 The Steiner ratio of dual planes; title: 9 THE STEINER RATIO AND THE; title: EMBEDDING OF SPACES; title: 9.1 Isometric Embeddings of Lp-spaces; title: 9.2 The Steiner Ratio for Banach-Minkowski Spaces of high; title: Dimensions; title: 10 THE STEINER RATIO AND DISCRETE; title: GEOMETRY; title: 10.1 Diameter and Radius, Equilateral sets; title: 10.2 Packings and Coverings; title: 10.3 Tammes' Problem; title: 11 THE DEPENDENCE OF THE STEINER; title: RATIO ON THE DIMENSION; title: 11.1 A list of the Steiner ratio of Banach-Minkowski planes; title: 11.2 When the dimension jumps from two to three; title: 11.3 When the dimension runs to infinity; title: 12 RELATED QUESTIONS; title: 12.1 A Finite Number of Points inside a compact set; title: 12.2 The Steiner Ratio for k-SMT's; title: 12.3 Steiner's Problem with weighted nodes; title: 12.4 Greedy Trees; title: 12.5 Component-size bounded Steiner Trees; title: 12.6 Shortest multiple-edge-connected networks; title: REFERENCES; title: INDEX.