Hypervelocity information extraction from huge informations

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We investigated fast algorithms for treating big data, and lower bounds about them. Especially, algorithms that see only constant number of data of the given instance are mainly investigated. We obtained fast constant-time algorithms for approximating the size of the maximum independent set and the maximum matching of graphs, a testing outerplanarity of graphs, approximating the rank of sparsity matroids, and approximating the solution of the knapsack problem. And we presented new tools for showing linear lower bounds for testing algorithms. Moreover, we considered to parametrize unit disk graphs by the area, and gave some FPT algorithms and lower bounds on some problems on them.