A practical approximation algorithm for the LMS line estimator

The problem of fitting a straight line to a finite collection of points in the plane is an important problem in statistical estimation. Robust estimators are widely used because of their lack of sensitivity to outlying data points. The least median-of-squares (LMS) regression line estimator is among the best known robust estimators. Given a set of n points in the plane, it is defined to be the line that minimizes the median squared residual or, more generally, the line that minimizes the residual of any given quantile q, where 0<q?1. This problem is equivalent to finding the strip defined by two parallel lines of minimum vertical separation that encloses at least half of the points.The best known exact algorithm for this problem runs in O(n²) time. We consider two types of approximations, a residual approximation, which approximates the vertical height of the strip to within a given error bound ε_r?0, and a quantile approximation, which approximates the fraction of points that lie within the strip to within a given error bound ε_q?0. We present two randomized approximation algorithms for the LMS line estimator. The first is a conceptually simple quantile approximation algorithm, which given fixed q and ε_q>0 runs in O(nlogn) time. The second is a practical algorithm, which can solve both types of approximation problems or be used as an exact algorithm. We prove that when used as a quantile approximation, this algorithm's expected running time is . We present empirical evidence that the latter algorithm is quite efficient for a wide variety of input distributions, even when used as an exact algorithm.     

Heuristic Algorithms for Determination of Canonical Forms and Grammatical Characteristics of Words

Algorithms are developed that determine canonic forms and grammar categories from individual words and the vocabulary of a text. Algorithms are proved to be highly efficient. The accuracy of determination directly depends on the length of the text.     

Using Vapnik–Chervonenkis Dimension to Analyze the Testing Complexity of Program Segments

We examine the complexity of testing different program constructs. We do this by defining a measure of testing complexity known as VCP-dimension, which is similar to the Vapnik–Chervonenkis dimension, and applying it to classes of programs, where all programs in a class share the same syntactic structure. VCP-dimension gives bounds on the number of test points needed to determine that a program is approximately correct, so by studying it for a class of programs we gain insight into the difficulty of testing the program construct represented by the class. We investigate the VCP-dimension of straight line code, if–then–else statements, and for loops. We also compare the VCP-dimension of nested and sequential if–then–else statements as well as that of two types of for loops with embedded if–then–else statements. Finally, we perform an empirical study to estimate the expected complexity of straight line code.     

Case study: Treatment of herpes genitalis phobia and agoraphobia with panic attacks.

A 25-yr-old woman with incapacitating hypochondriasis (disease phobia and conviction of being infected with herpes genitalis) for 4 yrs and agoraphobia with panic attacks for 2 yrs was well after 6 mo of treatment and at 14-mo follow-up. Agoraphobia was treated with a combination of desensitization in imagery, aided by relaxation training using electromyogram (EMG) and skin temperature biofeedback, followed by exposure in vivo. Hypochondriasis was treated by psychotherapeutic techniques and presentation of medical facts. (20 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

International Handbook of Urban Policy,Volume 1: Contentious Global Issues

Abstract

From the Review Editors

Place Making: Developing Town Centers, Main Streets, and Urban Villages Charles C. Bohl. Urban Land Institute, Washington, DC, 2002. 305 pages. $69.95.

Redesigning Cities: Principles, Practice, Implementation Jonathan Barnett. APA Planners Press, Chicago, 2003. 312 pages. $45.95.

Principles of Emergency Planning and Management David Alexander. Oxford University Press, New York, 2002. 304 pages. $30 (paperback).

Environmental Politics and Policy in Industrialized Countries Uday Desai, editor. MIT Press, Cambridge, MA, 2002. 403 pages. $62, $24.95 (paperback).

New Technologies, Economies, and Communities

New Money, Nice Town: How Capital Works in the New Urban Economy Leonard Nevarez. Routledge, New York, 2003. 224 pages. $22.95 (paperback).

Information and Communication Technologies and Rural Development Organisation for Economic Cooperation and Development (OECD). OECD, Paris, 2001. 191 pages. $27.

The Co-Workplace: Teleworking in the Neighborhood Laura Johnson. University of British Columbia Press, Vancouver, BC, 2003. 144 pages. $85.

Wired to the World, Chained to the Home: Telework in Daily Life Penny Gurstein. University of British Columbia Press, Vancouver, BC, 2001. 246 pages. $75.

Global Decisions, Local Collisions: Urban Life in the New World Order David Ranney. Temple University Press, Philadelphia, 2003. $69.50, $19.95 (paperback).

Bridging the Digital Divide: Technology, Community and Public Policy Lisa J. Servon. Blackwell Publishing, Malden, MA, 2002. 273 pages. $27.95.

Empire City: The Making and Meaning of the New York City Landscape David M. Scobey. Temple University Press, Philadelphia, 2002. 340 pages. $40.

Building Chicago: The First Hundred Years [Video]. Films for the Humanities &; Sciences (producer). Princeton, NJ, 1997. 30 minutes $129.95.

Paris in the 19th Century: The Making of a Modern City [Video]. Films for the Humanities &; Sciences (producer). Princeton, NJ, 1998. 58 minutes $149.95.

Democracy in Practice: Public Participation in Environmental Decisions Thomas C. Beierle and Jerry Cayford. Resources for the Future, Washington, DC, 2002. 147 pages. $50, $18.95 (paperback).

Successful Public Meetings: A Practical Guide Elaine Cogan. American Planning Association, Chicago, 2000. 134 pages. $22.95.

The Elusive Quest for Growth: Economists' Adventures and Misadventures in the Tropics William Easterly. MIT Press, Cambridge, MA, 2002. 356 pages. $17.95.

American Metropolitics: The New Suburban Reality Myron Orfield. Brookings Institution Press, Baltimore, 2002. 221 pages. $29.95.

Place Matters: Metropolitics for the 21st Century Peter Dreier, John Mollenkopf, and Todd Swanstrom. University of Kansas Press, Lawrence, 2001. 349 pages. $15.95.

Land Use Planning Made Plain, 2nd Edition Hok-Lin Leung. University of Toronto Press, Toronto, 2003. 292 pages. $29.95 (paperback).

Ecology, Engineering, and Management: Reconciling Ecosystem Rehabilitation and Service Reliability Michel van Eeten and Emery Roe. Oxford University Press, New York, 2002. 268 pages. $50.

Ecological Planning: A Historical and Comparative Synthesis Forster Ndubisi. Johns Hopkins University Press, Baltimore, 2002. 286 pages. $45.

Developing Successful Infill Housing Diane R. Suchman. Urban Land Institute, Washington, DC, 2002. 202 pages. $59.95 (paperback).

Time-Saver Standards for Urban Design Donald Watson, Alan Plattus, and Robert Shibley. McGraw-Hill, New York, 2003. 960 pages. $150.

A Limited Partnership: The Politics of Religion, Welfare, and Social Service Bob Wineburg. Columbia University Press, New York, 2001. 229 pages. $51, $23.50 (paperback).

Urban Indicators for Managing Cities (Cities Data Book) Matthew S. Westfall and Victoria A. de Villa. Asian Development Bank, Manila, 2001. 460 pages and CD. $30.

The World's Water: The Biennial Report on Freshwater Resources 2002–2003 Peter Gleick with William C. G. Burns, Elizabeth L. Chalecki, Michael Cohen, Katherine Kao Cushing, Amar S. Mann, Rachel Reyes, Gary H. Wolff, and Arlene K. Wong. Island Press, Washington DC, 2002. 334 pages. $32.50.

OECD Environmental Indicators: Toward Sustainable Development Organisation for Economic Co-operation and Development (OECD). OECD, Paris, 2001. 155 pages. $27.

The State of the Nation's Ecosystems: Measuring the Lands, Waters, and Living Resources of the United States H. John Heinz III Center for Science, Economics and the Environment. Cambridge University Press, Cambridge, UK, 2002. 270 pages. $25.     

Optimal Robot Localization in Trees

The problem of localization, that is, of a robot finding its position on a map, is an important task for autonomous mobile robots. It has applications in numerous areas of robotics ranging from aerial photography to autonomous vehicle exploration. In this paper we present a new strategy LPS (Localize-by-Placement-Separation) for a robot to find its position on a map, where the map is represented as a geometric tree of bounded degree. Our strategy exploits to a high degree the self-similarities that may occur in the environment. We use the framework of competitive analysis to analyze the performance of our strategy. In particular, we show that the distance traveled by the robot is at most O( ) times longer than the shortest possible route to localize the robot, where n is the number of vertices of the tree. This is a significant improvement over the best known previous bound of O(n^2/3). Moreover, since there is a lower bound of Ω( ), our strategy is optimal up to a constant factor. Using the same approach we can also show that the problem of searching for a target in a geometric tree, where the robot is given a map of the tree and the location of the target but does not know its own position, can be solved by a strategy with a competitive ratio of O( ), which is again optimal up to a constant factor.