Automated label placement in theory and practice
نویسنده
چکیده
v 1 An Introduction to Label Placement 1 1.1 Historic Development . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 . . . and Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.5 Future Development . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.6 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.6.1 General Labeling, Compatible Representatives, and CSP . 6 1.6.2 Point Labeling: Label-Number Maximization . . . . . . . 7 1.6.3 Point Labeling: Label-Size Maximization . . . . . . . . . 8 1.6.4 Line Labeling . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.6.5 Designing Geometric Algorithms . . . . . . . . . . . . . . 9 2 General Labeling: Label-Number Maximization 11 2.1 Label Placement and CSP . . . . . . . . . . . . . . . . . . . . . . 13 2.2 Maximum Variable-Subset CSP . . . . . . . . . . . . . . . . . . . 14 2.3 Irreducibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.4 An Edge-Irreducibility Algorithm . . . . . . . . . . . . . . . . . . 18 2.5 A General Label-Placement Algorithm . . . . . . . . . . . . . . . 28 3 Point Labeling: Label-Number Maximization 31 3.1 Comparing Various Models . . . . . . . . . . . . . . . . . . . . . 33 3.2 Fixed-Position Models . . . . . . . . . . . . . . . . . . . . . . . . 42 3.2.1 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.2.2 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.3 Slider Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.3.1 NP-Hardness . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.3.2 A Greedy Approximation Algorithm . . . . . . . . . . . . 65 3.3.3 A Polynomial Time Approximation Scheme . . . . . . . . 71 3.3.4 Implementation and Experimental Results . . . . . . . . . 75 4 Point Labeling: Label-Size Maximization 81 4.1 Rectangular Labels . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.2 Circular Labels . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.2.1 Previous Work . . . . . . . . . . . . . . . . . . . . . . . . 84 4.2.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . 84 4.2.3 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 4.2.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 4.2.5 NP-Hardness . . . . . . . . . . . . . . . . . . . . . . . . . 91
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