Property Testing and Combinatorial Approximation
نویسنده
چکیده
1 1 General introduction 3 1.1 Combinatorial property testing . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.1 Property testing in the dense graph (and hypergraph) model . . . . 4 1.1.2 Testing graph properties in other models . . . . . . . . . . . . . . . 5 1.1.3 Testing massively parameterized properties . . . . . . . . . . . . . . 5 1.2 Probabilistically checkable proofs of proximity PCPPs . . . . . . . . . . . 6 2 Summary of results 8 2.1 Testing graph isomorphism . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2 Approximate hypergraph partitioning and applications . . . . . . . . . . . . 8 2.3 Testing st-connectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.4 Testing orientations for being Eulerian . . . . . . . . . . . . . . . . . . . . . 9 2.5 Length-Soundness tradeoffs for 3-query PCPPs . . . . . . . . . . . . . . . . 10 3 Global definitions and preliminaries 11 3.1 General notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.2 Property testers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.3 Graphs and graph properties . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.3.1 Distance between graphs and properties . . . . . . . . . . . . . . . . 12 3.4 Restriction, variation distance and Yao’s method . . . . . . . . . . . . . . . 13 I Dense Graphs and Hypergraphs 14 4 Testing graph isomorphism 15 4.1 Background and introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.2 Specific definitions and preliminaries . . . . . . . . . . . . . . . . . . . . . . 17
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