This paper offers a path planning algorithm based on splines. The sought path avoids the obstacles, and is smooth and short. Smoothing is used as an integral part of the algorithm, and not only as a final improvement to a path found by other methods. In order to avoid a very difficult optimization over all the path's points, it is modeled by a sequence of splines defined by a gradually increasing number of knots

Property testing is a rapidly growing field of research. Typically, a property testing algorithm proceeds by quickly determining whether an input can satisfy some condition, under the assumption that most inputs do not satisfy it. If the input is "far” from satisfying the condition, the algorithm is guaranteed to reject it with high probability. Applying this paradigm to image detection is desirable since images are large objects and a lot of time can be saved by quickly rejecting images which are "far” from satisfying a certain condition the user is interested in. Further, typically most inputs are, indeed, "far” from the sought images. We demonstrate this by analyzing the problem of deciding whether a binary image can be partitioned according to a template represented by a rectangular grid, and introduce a quick "rejector,” which tests an image extracted from the input image, but whose size, as well as the time required to construct it, are constants which are independent of the input image size. With high probability, the rejector dismisses the inputs which are "far” from the template.

An important class of queries over sensor networks are network-wide aggregation queries. In this work we study a class of aggregation queries which we refer to as aggregate threshold queries. The goal of an aggregate threshold query is to continuously monitor the network and give a notification every time an aggregated value crosses a predetermined threshold value. Aggregate threshold queries are of particular importance in a wireless sensor environment, since they allow network-wide events to be detected, with a minimum expenditure of energy. Such network-wide events might include, for example, the variance in sensor readings exceeding a certain threshold. We present an efficient algorithm for implementing arbitrary aggregate threshold queries over sensor networks. Our algorithm is based on a novel geometric approach by which an arbitrary aggregate threshold query can be split into a set of numerical constraints on the readings of the individual sensors. These constraints are used by the individual sensors to monitor their readings. The constraints are constructed so that as long as none of the constraints are violated, it is guaranteed that the aggregated value has not crossed the threshold. Experiments we performed on real-world data indicate that by employing these constraints, sensors are able to reduce the number of transmissions required for implementing the query by orders of magnitude, thus significantly reducing energy consumption.