8530273
Drawing Planar Graphs with Large Vertices and Thick Edges
We consider the problem of representing size information in the edges and vertices of a planar graph. Such information can be used, for example, to depict a network of computers and information traveling through the network. We present an efficient linear-time algorithm which draws edges and vertices of varying 2-dimensional areas to represent the amount of information flowing through them. The algorithm avoids all occlusions of nodes and edges, while still drawing the graph on a compact integer grid.
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.
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.
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>).
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.
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
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.
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.
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.
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.
12614052
Learning haptic feedback for guiding driver behavior
Information about the driving state can be conveyed to automobile drivers through force feedback signals sent via the pedals and steering wheel. Because the set of possible haptic signals and driver responses is huge, it is desirable to automatically learn which signals are most useful to drivers. Thus, it is instructive to explore how machine learning techniques can be used as a step in the design of a haptic interface system. In this paper, we present a learning algorithm that learns useful haptic feedback and apply the algorithm to learning feedback for automobile drivers. We present evidence to show that the algorithm is sensitive enough to learn useful feedback under some circumstances, but that its scope may be limited by people's ability to act as admittance controllers.