Slides.

More documents

Recommendations

Info

STEPHAN KREUTZER COMPLEXITY OF MODEL-CHECKING PROBLEMS 4/81 INTRODUCTION COMPLEXITY UPPER BOUNDS COMPOSITION LOCALITY LOCALISATION GRIDS GRID-LIKE MINORS LABELLED WEBS A Connection to Complexity Theory Many standard computational problems on graphs are NP-complete, e.g. • Dominating Set (find a min. set of vertices neighbours to all others) • 3-Colourability (3-colour a graph without monochromatic edges) • Hamiltonian path (find a path containing every vertex exactly once) Study classes of graphs (planar graphs, graphs of bounded genus, ...) on which some of these problems become tractable. Logical approach. Instead of designing algorithms for each problem individually, formulate the problems in a logical language and design model-checking algorithms on these classes of graphs.
STEPHAN KREUTZER COMPLEXITY OF MODEL-CHECKING PROBLEMS 4/81 INTRODUCTION COMPLEXITY UPPER BOUNDS COMPOSITION LOCALITY LOCALISATION GRIDS GRID-LIKE MINORS LABELLED WEBS A Connection to Complexity Theory Many standard computational problems on graphs are NP-complete, e.g. • Dominating Set (find a min. set of vertices neighbours to all others) (Parametrized) definable in First-Order Logic (FO) • 3-Colourability (3-colour a graph without monochromatic edges) definable in Monadic Second-Order Logic (MSO) • Hamiltonian path (find a path containing every vertex exactly once) definable in Monadic Second-Order Logic (MSO 2 ) Study classes of graphs (planar graphs, graphs of bounded genus, ...) on which some of these problems become tractable. Logical approach. Instead of designing algorithms for each problem individually, formulate the problems in a logical language and design model-checking algorithms on these classes of graphs.
Page 1 and 2: Towards a Structural Characterisati
Page 3 and 4: STEPHAN KREUTZER COMPLEXITY OF MODE
Page 5: STEPHAN KREUTZER COMPLEXITY OF MODE
Page 57 and 58:
STEPHAN KREUTZER COMPLEXITY OF MODE
Page 59 and 60:
Page 61 and 62:
Page 63 and 64:
Page 65 and 66:
Page 67 and 68:
Page 69 and 70:
Page 71 and 72:
Page 73 and 74:
Page 75 and 76:
Page 77 and 78:
Page 79 and 80:
Page 81 and 82:
Page 83 and 84:
Page 85 and 86:
Page 87 and 88:
Page 89 and 90:
Page 91 and 92:
INTRODUCTION COMPLEXITY UPPER BOUND
Page 93 and 94:
Page 95 and 96:
Page 97 and 98:
Page 99 and 100:
Page 101 and 102:
Page 103 and 104:
Page 105 and 106:
Page 107 and 108:
Page 109 and 110:
Page 111 and 112:
Page 113 and 114:
Page 115 and 116:
Page 117 and 118:
Page 119 and 120:
Page 121 and 122:
Page 123 and 124:
Page 125 and 126:
Page 127 and 128:
Page 129 and 130:
Page 131 and 132:
Page 133 and 134:
Page 135 and 136:
Page 137 and 138:
Page 139 and 140:
Page 141 and 142:
Page 143 and 144:
Page 145 and 146:
Page 147 and 148:
Page 149 and 150:
Page 151 and 152:
Page 153 and 154:
Page 155 and 156:
Page 157 and 158:
show all

Slides.

Create successful ePaper yourself

Delete template?

Save as template?