Answering Conjunctive Queries under Updates

We consider the task of enumerating and counting answers to $k$-ary conjunctive queries against relational databases that may be updated by inserting or deleting tuples. We exhibit a new notion of q-hierarchical conjunctive queries and show that these can be maintained efficiently in the following sense. During a linear time preprocessing phase, we can build a data structure that enables constant delay enumeration of the query results; and when the database is updated, we can update the data structure and restart the enumeration phase within constant time. For the special case of self-join free conjunctive queries we obtain a dichotomy: if a query is not q-hierarchical, then query enumeration with sublinear$^\ast$ delay and sublinear update time (and arbitrary preprocessing time) is impossible. For answering Boolean conjunctive queries and for the more general problem of counting the number of solutions of k-ary queries we obtain complete dichotomies: if the query's homomorphic core is q-hierarchical, then size of the the query result can be computed in linear time and maintained with constant update time. Otherwise, the size of the query result cannot be maintained with sublinear update time. All our lower bounds rely on the OMv-conjecture, a conjecture on the hardness of online matrix-vector multiplication that has recently emerged in the field of fine-grained complexity to characterise the hardness of dynamic problems. The lower bound for the counting problem additionally relies on the orthogonal vectors conjecture, which in turn is implied by the strong exponential time hypothesis. $^\ast)$ By sublinear we mean $O(n^{1-\varepsilon})$ for some $\varepsilon>0$, where $n$ is the size of the active domain of the current database

Corruption level and uncertainty, FDI and domestic investment

Based on real options theory and institutional factors, we develop a theoretical framework for investment in the presence of corruption and use a sample of private firms in 13 European countries over 2001–2013 to carry out the first large-scale analysis of the impact of the level of corruption and uncertainty about corruption on post-entry investment of MNE subsidiaries. We employ several waves of managerial surveys (the Business Environment and Enterprise Performance Survey; BEEPS) to construct local- rather than merely country-level measures of corruption level and uncertainty. In combination with a large European firm-level database (Amadeus), we show that corruption uncertainty and corruption level do not have an effect on the investment of MNE subsidiaries. We next carry out the analysis on the sample of domestic firms and find a negative investment effect that is driven primarily by corruption uncertainty rather than corruption level. We also show that investment of domestic firms that are similar (matched) to MNE subsidiaries is unaffected directly by corruption, but is affected by uncertainties related to finances and judiciary. Our results are robust to controlling for various types of uncertainty, and they provide new insights into the effects of corruption on investment