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.
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
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.
70455
TRICERT: A Distributed Certified E-Mail Scheme
In this paper we present protocols for distributed certified e-mail, which use encryption to ensure both confidentiality and fairness. As with other protocols for certified e-mail, ours achieve fairness by placing trust on an external entity, referred to as the Trusted Third Party (TTP). The TTP can become a bottleneck, however, and we explore scenarios that support a distributed TTP, in the context of both off-line and online protocols. With several servers dividing the TTP responsibilities, the level of confidence placed in individual servers can be reduced without compromising the TTP’s overall trust.
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.
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.
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.
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.
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.
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.