34871033
Parallel Algorithms for Evaluating Sequences of Set-Manipulation Operations
Given an off-line sequence S of n set-manipulation operations, we investigate the parallel complexity of evaluating S (i.e. finding the response to every operation in S and returning the resulting set). We show that the problem of evaluating S is in NC for various combinations of common set-manipulation operations. Once we establish membership in NC (or, if membershp in NC is obvious), we develop techniques for improving the time and/or processor complexity.
15210615
An Improved Ray Shooting Method for Constructive Solid Geometry Models Via Tree Contraction
In the Constructive Solid Geometry (CSG) representation a geometric object is described as the hierarchical combination of a number of primitive shapes using the operations union, intersection, subtraction, and exclusive-union. This hierarchical description defines an expression tree, T, called the CSG tree, with leaves associated with primitive shapes, internal nodes associated with operations, and whose "value" is the geometric object. Evaluation of CSG trees is an important computation that arises in many rendering and analysis problems for geometric models, with ray shooting (also known as "ray casting") being one of the most important. Given any CSG tree T, which may be unbalanced, we show how to convert T into a functionally-equivalent binary tree, D, that is balanced. We demonstrate the utility of this conversion by showing how it can be used to improve the worst-case running time for ray shooting against a CSG model from O(n2) to O(n log n), which is optimal. In addition, the practicality of our method has been demonstrated in experimental benchmarking tests using the BRL-CAD package.
14228028
Efficient piecewise-linear function approximation using the uniform metric: (preliminary version)
We give an <italic>O</italic>(<italic>n</italic>log<italic>n</italic>)-time method for finding a best <italic>k</italic>-link piecewise-linear function approximating an <italic>n</italic>-point planar data set using the well-known uniform metric to measure the error, ε≥0, of the approximation. Our method is based upon new characterizations of such functions, which we exploit to design an efficient algorithm using a plane sweep in “ε space” followed by several applications of the parametric searching technique. The previous best running time for this problem was <italic>O</italic>(<italic>n</italic><supscrpt>2</supscrpt>).
8446216
Balanced aspect ratio trees: combining the advantages of k-d trees and octrees
Given a set S of n points on Rd, we show, for fixed d, how to construct in O(nlogn) time a data structure we call the balanced aspect ratio (BAR) tree. A BAR tree is a binary space partition tree on S that has O(logn) depth in which every region is convex and “fat” (that is, has a bounded aspect ratio). While previous hierarchical data structures such as k-d trees, quadtrees, octrees, fair-split trees, and balanced box decompositions can guarantee some of these properties, we know of no previous data structure that combines all of these properties simultaneously. The BAR tree data structure has numerous applications ranging from geometric searching problems in fixed dimensional space to the visualization of graphs and three-dimensional worlds.
13413744
Snap rounding line segments efficiently in two and three dimensions
We study the problem of robustly rounding a set S of n line segments in R2 using the snap rounding paradigm. In this paradigm each pixel containing an endpoint or intersection point is called “hot,” and all segments intersecting a hot pixel are re-routed to pass through its center. We show that a snap-rounded approximation to the arrangement defined by S can be built in an output-sensitive fashion, and that this can be done without first determining all the intersecting pairs of segments in S. Specifically, we give a deterministic plan~sweep algorithm running in time O(n bgn -F&H Ihl10g ~), where ~ is the set of hot pixela and \hl is the number of segments intersecting a hot pixel h E H. We also give a simple randomized incremental construction whose expected running time matches that of our deterministic algorithm. The complexity of these algorithms is optimal up to polylogarithmic factors. “This research is supported by NSF grant CCR9625289 and by U.S. ARO grsnt DAAH0496-1-O013. tThis rese~ch is supported by NSF grant CCR9623851 and US Army MUFU grant 5-23542-A. Permission 10make digil; llhd mpits tll’illl tw [ml o~lhis m:lterinl Ibr persomrl or Clossroom me is grnnled tvilllo{ll lid prnvidcrl 1}101Ihe copIcs are not mode nr distrihukd Ibr proli( or conm~L$rci.o I adwrnlngc. Ihc copy ri~l notice. Ihe tillc nl’the puhlicotion :Ind ih da(c ;Ippcilr. aml nn[iw IS given ihal cnpJTighl is h) pcrmissmn ol’lhc ,\(’il. [m. “1’0cnp) olhcn! M,. to rcpuhl ish. 10pnsl on swvers or It>rcdislrilw Ic Io Iisls. requires spwi Iic permission md~or tiec ( “ompttf{rfwndi ( ;wmcrr] 9Xii~.cl:r:m,c Copyrighl I 997 ,AChl 0M79 I-X78-997 ‘(I6,,S.75{1 LEONIDAS J. GUIBASt Dept. of Computer Science
1270229
Fast Randomized Parallel Methods for Planar Convex Hull Construction
Abstract We present a number of efficient parallel algorithms for constructing 2-dimensional convex hulls on a randomized CRCW PRAM. Specifically, we show how to build the convex hull of n presorted points in the plane in O(1) time using O(n log n) work, with n-exponential probability, or, alternately, in O ( log ∗ n) time using O(n) work, with n-exponential probability. We also show how to find the convex hull of n unsorted planar points in O(log n) time using O(n log h) work, with n-exponential probability, where h is the number of edges in the convex hull (h is O(n), but can be as small as O(1)). Our algorithm for unsorted inputs depends on the use of new in-place procedures, that is, procedures that are defined on a subset of elements in the input and that work without reordering the input. In order to achieve our n-exponential confidence bounds we use a new parallel technique called failure sweeping.
15752591
Satisficing anytime action search for behavior-based voting
Within the field of behavior-based robotics, a useful and popular technique for robot control is that of utilitarian voting, where behaviors representing objectives assign utilities to candidate actions. Utilitarian voting allows for distributed, modular control but is not well suited to systems with very high resolution or several, dependent degrees of freedom. Past systems have depended on exhaustive searches that choose the action with the highest combined utility. We present, instead, a framework that casts the action search problem as an anytime algorithm. This allows directed searches to be used with time limit constraints. Aspiration-based satisficing additionally helps to reduce CPU usage. In experiments so far, we have decreased CPU usage by UP to 42% while causing result quality to be no more than 6% worse.
17845810
A binary-categorization approach for classifying multiple-record Web documents using application ontologies and a probabilistic model
The amount of information available on the World Wide Web has been increasing dramatically in recent years. To enhance speedy searching and retrieving Web documents of interest, researchers and practitioners have partially relied on various information retrieval techniques. We propose a probabilistic model to classify Web documents into relevant documents and irrelevant documents with respect to a particular application ontology, which is a conceptual-model snippet of standard ontologies. Our probabilistic model is based on multivariate statistical analysis and is different from the conventional probabilistic information retrieval models. The experiments we have conducted on a set of representative Web documents indicate that the proposed probabilistic model is promising in binary-categorization of multiple-record Web documents.
1846400
Common metrics for human-robot interaction
This paper describes an effort to identify common metrics for task-oriented human-robot interaction (HRI). We begin by discussing the need for a toolkit of HRI metrics. We then describe the framework of our work and identify important biasing factors that must be taken into consideration. Finally, we present suggested common metrics for standardization and a case study. Preparation of a larger, more detailed toolkit is in progress.
29722627
A theory of satisficing decisions and control
The existence of an optimal control policy and the techniques for finding it are grounded fundamentally in a global perspective. These techniques can be of limited value when the global behaviour of the system is difficult to characterize, as it may be when the system is nonlinear, when the input is constrained, or when only partial information is available regarding system dynamics or the environment. Satisficing control theory is an alternative approach that is compatible with the limited rationality associated with such systems. This theory is extended by the introduction of the notion of strong satisficing to provide a systematic procedure for the design of satisficing controls. The power of the satisficing approach is illustrated by applications to representative control problems.
11363478
Learning To Cooperate in a Social Dilemma: A Satisficing Approach to Bargaining
Learning in many multi-agent settings is inherently repeated play. This calls into question the naive application of single play Nash equilibria in multi-agent learning and suggests, instead, the application of give-and-take principles of bargaining. We modify and analyze a satisficing algorithm based on (Karandikar et al., 1998) that is compatible with the bargaining perspective. This algorithm is a form of relaxation search that converges to a satisficing equilibrium without knowledge of game payoffs or other agents' actions. We then develop an M action, N player social dilemma that encodes the key elements of the Prisoner's Dilemma. This game is instructive because it characterizes social dilemmas with more than two agents and more than two choices. We show how several different multi-agent learning algorithms behave in this social dilemma, and demonstrate that the satisficing algorithm converges, with high probability, to a Pareto efficient solution in self play and to the single play Nash equilibrium against selfish agents. Finally, we present theoretical results that characterize the behavior of the algorithm.