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In this paper, we propose a new counting scheme for m n contingency tables. Our scheme is a modification of Dyer and Greenhill's scheme for two rowed contingency tables. We can estimate not only the sizes of error, but also the sizes of the bias of the number of tables obtained by our scheme, on the assumption that we have an approximate sampler.
Takahiro FUJITA Kohei HATANO Shuji KIJIMA Eiji TAKIMOTO
We consider combinatorial online prediction problems and propose a new construction method of efficient algorithms for the problems. One of the previous approaches to the problem is to apply online prediction method, in which two external procedures the projection and the metarounding are assumed to be implemented. In this work, we generalize the projection to multiple projections. As an application of our framework, we show an algorithm for an online job scheduling problem with a single machine with precedence constraints.