The update complexity of selection and related problems

We present a framework for computing with input data specified by intervals, representing uncertainty in the values of the input parameters. To compute a solution, the algorithm can query the input parameters that yield more refined estimates in form of sub-intervals and the objective is to minimize the number of queries. The previous approaches address the scenario where every query returns an exact value. Our framework is more general as it can deal with a wider variety of inputs and query responses and we establish interesting relationships between them that have not been investigated previously. Although some of the approaches of the previous restricted models can be adapted to the more general model, we require more sophisticated techniques for the analysis and we also obtain improved algorithms for the previous model. We address selection problems in the generalized model and show that there exist 2-update competitive algorithms that do not depend on the lengths or distribution of the sub-intervals and hold against the worst case adversary. We also obtain similar bounds on the competitive ratio for the MST problem in graphs

Round-competitive algorithms for uncertainty problems with parallel queries

In computing with explorable uncertainty, one considers problems where the values of some input elements are uncertain, typically represented as intervals, but can be obtained using queries. Previous work has considered query minimization in the settings where queries are asked sequentially (adaptive model) or all at once (non-adaptive model). We introduce a new model where k queries can be made in parallel in each round, and the goal is to minimize the number of query rounds. Using competitive analysis, we present upper and lower bounds on the number of query rounds required by any algorithm in comparison with the optimal number of query rounds for the given instance. Given a set of uncertain elements and a family of m subsets of that set, we study the problems of sorting all m subsets and of determining the minimum value (or the minimum element(s)) of each subset. We also study the selection problem, i.e., the problem of determining the i-th smallest value and identifying all elements with that value in a given set of uncertain elements. Our results include 2-round-competitive algorithms for sorting and selection and an algorithm for the minimum value problem that uses at most (2 + ε) · optk + O 1 ε · lg m query rounds for every 0 < ε < 1, where optk is the optimal number of query round

Expanding sensor networks to automate knowledge acquisition

The availability of accurate, low-cost sensors to scientists has resulted in widespread deployment in a variety of sporting and health environments. The sensor data output is often in a raw, proprietary or unstructured format. As a result, it is often difficult to query multiple sensors for complex properties or actions. In our research, we deploy a heterogeneous sensor network to detect the various biological and physiological properties in athletes during training activities. The goal for exercise physiologists is to quickly identify key intervals in exercise such as moments of stress or fatigue. This is not currently possible because of low level sensors and a lack of query language support. Thus, our motivation is to expand the sensor network with a contextual layer that enriches raw sensor data, so that it can be exploited by a high level query language. To achieve this, the domain expert specifies events in a tradiational event-condition-action format to deliver the required contextual enrichment