Abstract-Given a set of objects and a query q, a point p is called the reverse k nearest neighbor (RkNN) of q if q is one of the k closest objects of p. In this paper, we introduce the concept of influence zone which is the area such that every point inside this area is the RkNN of q and every point outside this area is not the RkNN. The influence zone has several applications in location based services, marketing and decision support systems. It can also be used to efficiently process RkNN queries. First, we present efficient algorithm to compute the influence zone. Then, based on the influence zone, we present efficient algorithms to process RkNN queries that significantly outperform existing best known techniques for both the snapshot and continuous RkNN queries. We also present a detailed theoretical analysis to analyse the area of the influence zone and IO costs of our RkNN processing algorithms. Our experiments demonstrate the accuracy of our theoretical analysis.

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The standardized precipitation index (SPI) is widely used in drought assessments due to its simple data requirement and multiscale characteristics. However, there are some uncertainties in the process of its calculation. This study, taking the Heihe River basin in northwest of China as the study area, mainly focuses on the uncertainty issues both in SPI calculation and in drought characteristics associated with the probability distributions and parameter estimation errors. Ten probability distributions (two-and three-parameter log-logistic and log-normal, generalized extreme value, Pearson type III, burr, gamma, inverse Gaussian, and Weibull) are employed to estimate the SPI. Maximum likelihood estimation is used to estimate distribution parameters. Randomly generating parameters based on the normality assumption is applied to quantify the uncertainty of parameter estimations. Results show that log-logistic-type distribution presents quite close performance with the benchmark gamma distribution and thus is recommended as an alternative in fitting the precipitation data over the study area. Effects of both uncertainty sources (probability distribution functions and parameter estimation errors) are more reflected on extreme droughts (extremely dry or wet). The more extreme the SPI value, the greater uncertainties caused by both sources. Furthermore, the drought characteristics vary a lot from different distributions and parameter errors. These findings highlight the importance of uncertainty analysis of drought assessments, given that most studies in climatology focus on extreme values for drought analysis.

We investigated, based on self‐determination theory (SDT), the impact of the functional meaning of monetary rewards on individuals' motivation and performance and further tested the role of the psychological needs as the underlying mechanism. In two experimental studies, we show that when presented in an autonomy‐supportive way, rewards lead participants to experience greater intrinsic motivation, which leads them to perform better, than when monetary rewards are presented in a controlling way. This is mediated by greater psychological need satisfaction, indicating that through greater feelings of competence, autonomy, and relatedness, individuals experience greater intrinsic motivation for the task at hand. Our findings suggest that rewards can have a distinct effect on individuals' motivation and performance depending on whether they take on an autonomy‐supportive or controlling meaning, thus providing empirical evidence for the theoretical and practical implications of SDT's concept of functional meaning of rewards. By highlighting the importance of this concept, this research contributes to our understanding of the effectiveness of such rewards in the workplace, suggesting that they can foster employee motivation and performance if organisations present them to employees in an autonomy‐supportive way to convey an informational meaning and positively contribute to their psychological need stisfaction.