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• 2001033741 contributor B8936768.
• 2001033741 created "c2001.".
• 2001033741 date "2001".
• 2001033741 date "c2001.".
• 2001033741 dateCopyrighted "c2001.".
• 2001033741 description "Includes bibliographical references (p. 223-239) and index.".
• 2001033741 description "Machine generated contents note: I -- I -- 1 THE HISTORICAL GENESIS -- 1.1 The Past -- 1.2 The Present -- 1.3 The Future -- 2 NETWORKS, SPACES AND ALGORITHMS -- 2.1 Networks -- 2.2 Spaces -- 2.3 The Algorithmic Complexity of finding a Minimum Span- -- ning Tree -- 2.4 Steiner's Problem -- 3 SHORTEST TREES IN METRIC SPACES - A -- SURVEY -- 3.1 Basic Properties of Steiner Minimal Trees in metric spaces -- 3.2 The Vertex-Degrees of shortest trees in Banach-Minkowski -- spaces -- 3.3 The location of the Steiner points - Fermat's Problem -- 3.4 Examples -- 4 THE STEINER RATIO OF METRIC SPACES -- 4.1 The range of the Steiner ratio -- 4.2 Approximations -- 4.3 The Steiner ratio of finite metric spaces -- 4.4 The space of all words: Phylogenetic spaces -- 5 THE STEINER RATIO OF BANACH- -- MINKOWSKI SPACES -- 5.1 Basic Properties -- 5.2 The Decomposition of SMT's -- 5.3 A Derivation of the Steiner ratio -- 5.4 Direct Calculations for Lp-planes -- 5.5 Direct Calculations for C3 -- 5.6 Direct Calculations for higher-dimensional Lp-spaces -- 6 EUCLIDEAN SPACES -- 6.1 Nontrivial lower and upper bounds -- 6.2 The Euclidean plane -- 6.3 The higher-dimensional case -- 6.4 The three-dimensional case -- 7 THE STEINER RATIO OF NEIGHBOURED -- SPACES -- 7.1 Neighboured Banach-Minkowski spaces -- 7.2 Metrics in the Hyperspace -- 7.3 Estimating Steiner ratios using the Banach-Mazur distance -- 7.4 Estimating Steiner ratios using the Hausdorff distance -- 8 BANACH-MINKOWSKI PLANES -- 8.1 The Steiner ratio of the rectilinear plane -- 8.2 The Steiner ratio of A-geometries -- 8.3 A sharp lower bound for the Steiner ratio -- 8.4 The range of the Steiner ratio in planes -- 8.5 The Steiner ratio of dual planes -- 9 THE STEINER RATIO AND THE -- EMBEDDING OF SPACES -- 9.1 Isometric Embeddings of Lp-spaces -- 9.2 The Steiner Ratio for Banach-Minkowski Spaces of high -- Dimensions -- 10 THE STEINER RATIO AND DISCRETE -- GEOMETRY -- 10.1 Diameter and Radius, Equilateral sets -- 10.2 Packings and Coverings -- 10.3 Tammes' Problem -- 11 THE DEPENDENCE OF THE STEINER -- RATIO ON THE DIMENSION -- 11.1 A list of the Steiner ratio of Banach-Minkowski planes -- 11.2 When the dimension jumps from two to three -- 11.3 When the dimension runs to infinity -- 12 RELATED QUESTIONS -- 12.1 A Finite Number of Points inside a compact set -- 12.2 The Steiner Ratio for k-SMT's -- 12.3 Steiner's Problem with weighted nodes -- 12.4 Greedy Trees -- 12.5 Component-size bounded Steiner Trees -- 12.6 Shortest multiple-edge-connected networks -- REFERENCES -- INDEX.".
• 2001033741 extent "xi, 244 p. :".
• 2001033741 identifier "0792370155 (alk. paper)".
• 2001033741 identifier 2001033741-d.html.
• 2001033741 identifier 2001033741.html.
• 2001033741 isPartOf "Combinatorial optimization ; v. 10".
• 2001033741 issued "2001".
• 2001033741 issued "c2001.".
• 2001033741 language "eng".
• 2001033741 publisher "Dordrecht ; Boston : Kluwer Academic Pub.,".
• 2001033741 subject "511/.5 21".
• 2001033741 subject "QA166.3 .C55 2001".
• 2001033741 subject "Steiner systems.".
• 2001033741 tableOfContents "Machine generated contents note: I -- I -- 1 THE HISTORICAL GENESIS -- 1.1 The Past -- 1.2 The Present -- 1.3 The Future -- 2 NETWORKS, SPACES AND ALGORITHMS -- 2.1 Networks -- 2.2 Spaces -- 2.3 The Algorithmic Complexity of finding a Minimum Span- -- ning Tree -- 2.4 Steiner's Problem -- 3 SHORTEST TREES IN METRIC SPACES - A -- SURVEY -- 3.1 Basic Properties of Steiner Minimal Trees in metric spaces -- 3.2 The Vertex-Degrees of shortest trees in Banach-Minkowski -- spaces -- 3.3 The location of the Steiner points - Fermat's Problem -- 3.4 Examples -- 4 THE STEINER RATIO OF METRIC SPACES -- 4.1 The range of the Steiner ratio -- 4.2 Approximations -- 4.3 The Steiner ratio of finite metric spaces -- 4.4 The space of all words: Phylogenetic spaces -- 5 THE STEINER RATIO OF BANACH- -- MINKOWSKI SPACES -- 5.1 Basic Properties -- 5.2 The Decomposition of SMT's -- 5.3 A Derivation of the Steiner ratio -- 5.4 Direct Calculations for Lp-planes -- 5.5 Direct Calculations for C3 -- 5.6 Direct Calculations for higher-dimensional Lp-spaces -- 6 EUCLIDEAN SPACES -- 6.1 Nontrivial lower and upper bounds -- 6.2 The Euclidean plane -- 6.3 The higher-dimensional case -- 6.4 The three-dimensional case -- 7 THE STEINER RATIO OF NEIGHBOURED -- SPACES -- 7.1 Neighboured Banach-Minkowski spaces -- 7.2 Metrics in the Hyperspace -- 7.3 Estimating Steiner ratios using the Banach-Mazur distance -- 7.4 Estimating Steiner ratios using the Hausdorff distance -- 8 BANACH-MINKOWSKI PLANES -- 8.1 The Steiner ratio of the rectilinear plane -- 8.2 The Steiner ratio of A-geometries -- 8.3 A sharp lower bound for the Steiner ratio -- 8.4 The range of the Steiner ratio in planes -- 8.5 The Steiner ratio of dual planes -- 9 THE STEINER RATIO AND THE -- EMBEDDING OF SPACES -- 9.1 Isometric Embeddings of Lp-spaces -- 9.2 The Steiner Ratio for Banach-Minkowski Spaces of high -- Dimensions -- 10 THE STEINER RATIO AND DISCRETE -- GEOMETRY -- 10.1 Diameter and Radius, Equilateral sets -- 10.2 Packings and Coverings -- 10.3 Tammes' Problem -- 11 THE DEPENDENCE OF THE STEINER -- RATIO ON THE DIMENSION -- 11.1 A list of the Steiner ratio of Banach-Minkowski planes -- 11.2 When the dimension jumps from two to three -- 11.3 When the dimension runs to infinity -- 12 RELATED QUESTIONS -- 12.1 A Finite Number of Points inside a compact set -- 12.2 The Steiner Ratio for k-SMT's -- 12.3 Steiner's Problem with weighted nodes -- 12.4 Greedy Trees -- 12.5 Component-size bounded Steiner Trees -- 12.6 Shortest multiple-edge-connected networks -- REFERENCES -- INDEX.".
• 2001033741 title "The Steiner ratio / by Dietmar Cieslik.".
• 2001033741 type "text".