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>).
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.
14677263
Teaching the analysis of algorithms with visual proofs
We describe an approach for visually teaching important proofs in the Junior-Senior level course on the design and analysis of data structures and algorithms (CS7/DS&amp;A). The main idea of this educational paradigm is to justify important claims about data structures and algorithms by using pictures that visualize proofs so clearly that the pictures can qualify as proofs themselves. The advantage of using this approach for DS&amp;A is that it augments or even replaces inductive arguments that many students find difficult. Moreover, this paradigm communicates important algorithmic facts in a compelling way for students who are more visually-oriented. We illustrate this technique by giving examples of visual proofs of several key concepts in DS&amp;A.
8676248
Authenticated Dictionaries for Fresh Attribute Credentials
We describe several schemes for efficiently populating an authenticated dictionary with fresh credentials. The thrust of this effort is directed at allowing for many data authors, called sources, to collectively publish information to a common repository, which is then distributed throughout a network to allow for authenticated queries on this information. Authors are assured of their contributions being added to the repository based on cryptographic receipts that the repository returns after performing the updates sent by an author. While our motivation here is the dissemination of credential status data from multiple credential issuers, applications of this technology also include time stamping of documents, document version integrity control, and multiple-CA certificate revocation management, to name just a few.
15586236
Optimizing Area and Aspect Ratio in Straight-Line Orthogonal Tree Drawings
We investigate the problem of drawing an arbitrary n-node binary tree orthogonally in an integer grid using straight-line edges. We show that one can simultaneously achieve good area bounds while also allowing the aspect ratio to be chosen as being O(1) or sometimes even an arbitrary parameter. In addition, we show that one can also achieve an additional desirable aesthetic criterion, which we call “subtree separation.” We investigate both upward and non-upward drawings, achieving area bounds of O(n log n) and O(n log log n), respectively, and we show that, at least in the case of upward drawings, our area bound is optimal to within constant factors.
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.
43673902
Coordinated target assignment and intercept for unmanned air vehicles
Presents an end-to-end solution to the battlefield scenario where M unmanned air vehicles are assigned to strike N known targets, in the presence of dynamic threats. The problem is decomposed into the subproblems of (1) cooperative target assignment, (2) coordinated UAV intercept, (3) path planning, and (4) feasible trajectory generation. The design technique is based on a hierarchical approach to coordinated control. Detailed simulation results are presented.
13562077
Satisficing Equilibria: A Non-Classical Theory of Games and Decisions
Satisficing, or being “good enough,” is the fundamental obligation of rational decision makers. We cannot rationally choose an option, even when we do not know of anything better, unless we know it is good enough. Unfortunately, we are not often in the position of knowing that there could be no better option, and hence that the option must be good enough. A complete search through all logical possibilities is often impractical, particularly in multi-agent contexts, due to excessive computational difficulty, modeling complexity, and uncertainty. It can be equally impractical, if it is even possible, to determine the cost of the additional required search to find an option that is good enough. In a departure from the traditional notion of satisficing as a species of bounded rationality, satisficing is here redefined in terms of a notion of intrinsic rationality. Epistemic utility theory serves as the philosophical foundation of a new praxeological decision-making paradigm of satisficing equilibria that is applicable to both single- and multiple-agent scenarios. All interagent relationships are modeled by an interdependence function that explicitly accommodates both self and group interest, from which multilateral and unilateral selectability and rejectability mass functions can be derived and compared via the praxeic likelihood ratio test.
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.
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.