8026210
Offset-polygon annulus placement problems
The @d-annulus of a polygon P is the closed region containing all points in the plane at distance at most @d from the boundary of P. An inner (resp., outer) @d-offset polygon is the polygon defined by the inner (resp., outer) boundary of its @d-annulus. In this paper we address three major problems of covering a given point set S by an offset version or a polygonal annulus of a polygon P. First, the Maximum Cover objective is, given a value of @d, to cover as many points from S as possible by the @d-offset (or by the @d-annulus) of P, allowing translation and rotation. Second, the Containment problem is to minimize the value of @d such that there is a rigid transformation of the @d-offset (or the @d-annulus) of P that covers all points from S. Third, in the Partial Containment problem we seek the minimum offset of P covering k=<|S| points. These problems arise in many applications where one needs to match a given polygonal figure (a known model) to a set of points (usually, obtained measures). We address several variants of these problems, including convex and simple polygons, as well as polygons with holes and sets of polygons, and obtain algorithms with low-degree polynomial running times in all cases.
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>).
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.
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.
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.
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.
451273
Comparing the usefulness of video and map information in navigation tasks
One of the fundamental aspects of robot teleoperation is the ability to successfully navigate a robot through an environment. We define successful navigation to mean that the robot minimizes collisions and arrives at the destination in a timely manner. Often video and map information is presented to a robot operator to aid in navigation tasks. This paper addresses the usefulness of map and video information in a navigation task by comparing a side-by-side (2D) representation and an integrated (3D) representation in both a simulated and a real world study. The results suggest that sometimes video is more helpful than a map and other times a map is more helpful than video. From a design perspective, an integrated representation seems to help navigation more than placing map and video side-by-side.
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.
6463761
Snapshots for semantic maps
A significant area of research in mobile robotics is in the local representation of a remote environment. In order to include a human in a mobile robot task it becomes important to present the remote information efficiently to a human. A relatively new approach to information presentation is semantic maps. Semantic maps provide more detail about an environment than typical maps because they are augmented by icons or symbols that provide meaning for places or objects of interest. In this paper we present snapshot technology as a means to take pictures from the real world and store them in a semantic map. To make the snapshots and semantic map available to an operator, we identify and discuss general attributes for useful displays and present a mixed reality 3D interface that meets the requirements. The interface and snapshot technology are validated through experiments in real and simulated environments.
44773632
Satisficing Games
Optimization is a mathematical sophistication of the common sense view that decision makers ought to do the best they can, and leads to well known solution concepts for mathematical games. For multi-agent systems in naturalistic settings, however, uncertainty and complexity may subordinate optimal performance to the more moderate goals of functionality and robustness. Moderation is another common sense idea that can be made mathematically precise by defining a notion of comparative rationality, leading to a theory of satisficing games. Preferences in an m-agent satisficing game are characterized by a 2m-dimensional interdependence function, from which the joint m-dimensional gains and losses of the agent system can be derived and compared to determine the set of jointly satisficing decisions. This paradigm permits decision makers in the presence of uncertainty to consider multiple sets of possible actions and make decisions that are both robust and functional. Two well-known games, Prisoner's Dilemma and Battle of the Sexes, are analyzed from this, point of view.