Masking failures of multidimensional sensors (extended abstract)

When a computer monitors a physical process, the computer uses sensors to determine the values of the physical variables that represent the state of the process. A sensor can sometimes fail, however, and in the worst case report a value completely unrelated to the true physical value. The work described is motivated by a methodology for transforming a process control program that can not tolerate sensor failure into one that can. In this methodology, a reliable abstract sensor is created by combining information from several real sensors that measure the same physical value. To be useful, an abstract sensor must deliver reasonably accurate information at reasonable computational cost. Sensors are considered that deliver multidimensional values (e.g., location or velocity in three dimensions, or both temperature and pressure). Geometric techniques are used to derive upper bounds on abstract sensor accuracy and to develop efficient algorithms for implementing abstract sensors

Building Voronoi Diagrams for Convex Polygons in Linear Expected Time

Let P be a list of points in the plane such that the points of P taken in order form the vertices of a convex polygon. We introduce a simple, linear expected-time algorithm for finding the Voronoi diagram of the points in P. Unlike previous results on expected-time algorithms for Voronoi diagrams, this method does not require any assumptions about the distribution of points. With minor modifications, this method can be used to design fast algorithms for certain problems involving unrestricted sets of points. For example, fast expected-time algorithms can be designed to delete a point from a Voronoi diagram, to build an order k Voronoi diagram for an arbitrary set of points, and to determine the smallest enclosing circle for points at the vertices of a convex hull

There is a Planar Graph Almost as Good as the Complete Graph

Given a set S of points in the plane, there is a triangulation of S such that a path found within this triangulation has length bounded by a constant times the straight-line distance between the endpoints of the path. Specifically, for any two points a and b of S there is a path along edges of the triangulation with length less that sqrt(10) times [ab], where [ab] is the straight-line Euclidean distance between a and b. The triangulation that has this property is the L1 metric Delauney triangulation for the set S. This result can be applied to motion planning in the plane. Given a source, a destination, and a set of polygonal obstacles of size n, an O(n) size data structure can be used to find a reasonable approximation to the shortest path between the source and the destination in O (n log n) time

Planar Graphs and Sparse Graphs from Efficient Motion Planning in the Plane

Given a source, a destination, and a number of obstacles in the plane, the Motion Planning Program is to determine the best path to move an object (a robot) from the source to the destination without colliding with any of the obstacles. For us, motion is restricted to the plane, the robot is represented by a point, and the obstacles are represented by a set of polygons with a total of n vertices among all the polygonal obstacles

Term Reduction Using Directed Congruence Closure

Many problems in computer science can be described in terms of reduction rules that tell how to transform terms. Problems that can be handled in this way include interpreting programs, implementing abstract data types, and proving certain kinds of theorems. A terms is said to have a normal form if it can be transformed, using the reduction rules, into a term to which no further reduction rules apply. In this paper, we extend the Congruence Closure Algorithm, an algorithm for finding the consequences of a finite set of equations, to develop Directed Congruence Closure, a technique for finding the normal form of a term provided the reduction rules satisfy the conditions for a regular term rewriting system. This technique is particularly efficient because it inherits, from the Congruence Closure Algorithm, the ability to remember all objects that have already been proved equivalent

End-to-End Bayesian Segmentation and Similarity Assessment of Performed Music Tempo and Dynamics without Score Information

Segmenting continuous sensory input into coherent segments and subsegments is an important part of perception. Music is no exception. By shaping the acoustic properties of music during performance, musicians can strongly influence the perceived segmentation. Two main techniques musicians employ are the modulation of tempo and dynamics. Such variations carry important information for segmentation and lend themselves well to numerical analysis methods. In this article, based on tempo or loudness modulations alone, we propose a novel end-to-end Bayesian framework using dynamic programming to retrieve a musician's expressed segmentation. The method computes the credence of all possible segmentations of the recorded performance. The output is summarized in two forms: as a beat-by-beat profile revealing the posterior credence of plausible boundaries, and as expanded credence segment maps, a novel representation that converts readily to a segmentation lattice but retains information about the posterior uncertainty on the exact position of segments’ endpoints. To compare any two segmentation profiles, we introduce a method based on unbalanced optimal transport. Experimental results on the MazurkaBL dataset show that despite the drastic dimension reduction from the input data, the segmentation recovery is sufficient for deriving musical insights from comparative examination of recorded performances. This Bayesian segmentation method thus offers an alternative to binary boundary detection and finds multiple hypotheses fitting information from recorded music performances