Efficient MaxCount and threshold operators of moving objects

Calculating operators of continuously moving objects presents some unique challenges, especially when the operators involve aggregation or the concept of congestion, which happens when the number of moving objects in a changing or dynamic query space exceeds some threshold value. This paper presents the following six d-dimensional moving object operators: (1) MaxCount (or MinCount), which finds the Maximum (or Minimum) number of moving objects simultaneously present in the dynamic query space at any time during the query time interval. (2) CountRange, which finds a count of point objects whose trajectories intersect the dynamic query space during the query time interval. (3) ThresholdRange, which finds the set of time intervals during which the dynamic query space is congested. (4) ThresholdSum, which finds the total length of all the time intervals during which the dynamic query space is congested. (5) ThresholdCount, which finds the number of disjoint time intervals during which the dynamic query space is congested. And (6) ThresholdAverage, which finds the average length of time of all the time intervals when the dynamic query space is congested. For these operators separate algorithms are given to find only estimate or only precise values. Experimental results from more than 7,500 queries indicate that the estimation algorithms produce fast, efficient results with error under 5%

Efficient discrete-time simulations of continuous-time quantum query algorithms

The continuous-time query model is a variant of the discrete query model in which queries can be interleaved with known operations (called "driving operations") continuously in time. Interesting algorithms have been discovered in this model, such as an algorithm for evaluating nand trees more efficiently than any classical algorithm. Subsequent work has shown that there also exists an efficient algorithm for nand trees in the discrete query model; however, there is no efficient conversion known for continuous-time query algorithms for arbitrary problems. We show that any quantum algorithm in the continuous-time query model whose total query time is T can be simulated by a quantum algorithm in the discrete query model that makes O[T log(T) / log(log(T))] queries. This is the first upper bound that is independent of the driving operations (i.e., it holds even if the norm of the driving Hamiltonian is very large). A corollary is that any lower bound of T queries for a problem in the discrete-time query model immediately carries over to a lower bound of \Omega[T log(log(T))/log (T)] in the continuous-time query model.Comment: 12 pages, 6 fig

On Stabbing Queries for Generalized Longest Repeat

A longest repeat query on a string, motivated by its applications in many subfields including computational biology, asks for the longest repetitive substring(s) covering a particular string position (point query). In this paper, we extend the longest repeat query from point query to \emph{interval query}, allowing the search for longest repeat(s) covering any position interval, and thus significantly improve the usability of the solution. Our method for interval query takes a different approach using the insight from a recent work on \emph{shortest unique substrings} [1], as the prior work's approach for point query becomes infeasible in the setting of interval query. Using the critical insight from [1], we propose an indexing structure, which can be constructed in the optimal $O(n)$ time and space for a string of size $n$, such that any future interval query can be answered in $O(1)$ time. Further, our solution can find \emph{all} longest repeats covering any given interval using optimal $O(occ)$ time, where $occ$ is the number of longest repeats covering that given interval, whereas the prior $O(n)$-time and space work can find only one candidate for each point query. Experiments with real-world biological data show that our proposal is competitive with prior works, both time and space wise, while providing with the new functionality of interval queries as opposed to point queries provided by prior works.Comment: 10 page

An optimal query assignment for wireless sensor networks

With the increased use of large-scale real-time embedded sensor networks, new control mechanisms are needed to avoid congestion and meet required Quality of Service (QoS) levels. In this paper, we propose a Markov Decision Problem (MDP) to prescribe an optimal query assignment strategy that achieves a trade-off between two QoS requirements: query response time and data validity. Query response time is the time that queries spend in the sensor network until they are solved. Data validity (freshness) indicates the time elapsed between data acquisition and query response and whether that time period exceeds a predefined tolerance. We assess the performance of the proposed model by means of a discrete event simulation. Compared with three other heuristics, derived from practical assignment strategies, the proposed policy performs better in terms of average assignment costs. Also in the case of real query traffic simulations, results show that the proposed policy achieves cost gains compared with the other heuristics considered. The results provide useful insight into deriving simple assignment strategies that can be easily used in practice

Bipolar querying of valid-time intervals subject to uncertainty

Databases model parts of reality by containing data representing properties of real-world objects or concepts. Often, some of these properties are time-related. Thus, databases often contain data representing time-related information. However, as they may be produced by humans, such data or information may contain imperfections like uncertainties. An important purpose of databases is to allow their data to be queried, to allow access to the information these data represent. Users may do this using queries, in which they describe their preferences concerning the data they are (not) interested in. Because users may have both positive and negative such preferences, they may want to query databases in a bipolar way. Such preferences may also have a temporal nature, but, traditionally, temporal query conditions are handled specifically. In this paper, a novel technique is presented to query a valid-time relation containing uncertain valid-time data in a bipolar way, which allows the query to have a single bipolar temporal query condition