As of 2005, sampling has been incorporated in all major database systems. While efficient sampling techniques are realizable, determining the accuracy of an estimate obtained from the sample is still an unresolved problem. In this paper, we present a theoretical framework that allows an elegant treatment of the problem. We base our work on generalized uniform sampling (GUS), a class of sampling methods that subsumes a wide variety of sampling techniques. We introduce a key notion of equivalence that allows GUS sampling operators to commute with selection and join, and derivation of confidence intervals. We illustrate the theory through extensive examples and give indications on how to use it to provide meaningful estimates in database systems.

The task of routing in epidemic networks faces certain difficulties involving minimizing the delivery delay with a reduced consumption of resources. Every node has severe power constraints and the network is also susceptible to temporary but random failure of nodes. In the previous work, the parameter of mobility has been considered a constant for a certain setting. In our setting, we consider a varying parameter of mobility. In this framework, we determine the optimal mobility pattern and a forwarding policy that a network should follow in order to meet the trade-off between delivery delay and power consumption. In addition, the mobility pattern should be such that it can be practically incorporated. In this paper, we formulate an optimization problem which is solved by using the principles of dynamic programming. The resultant strategy, OFACT optimal forwarding algorithm with controlled transmission range, has been studied through extensive simulations. The performance of OFACT has been compared with a few existing strategies. Our results show that this optimization problem has a global solution.